`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`
${elem} `); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`
${book_segment.title} `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`
${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "WJuUcEXlLW41XFEN9ypxjk4IvBGgDetTk1uI3OEfqjkyq7Xhd248w2xHpwRvgQrO"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j
Solutions
Textbooks
`); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(` Solutions ${viewAllHTML} `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+" "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(` Textbooks View All `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; const user_hash = null; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_'+(is_login?user_hash:'ANON'))); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { if (is_login) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (prebooks.time && new Date().getTime()-prebooks.time<1000*60*60*6) { build_popup(); return; } } else { anon_pretype(); return; } } $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "WJuUcEXlLW41XFEN9ypxjk4IvBGgDetTk1uI3OEfqjkyq7Xhd248w2xHpwRvgQrO"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; if (is_login) { localStorage.setItem('PRETYPE_BOOKS_'+user_hash, JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books, time: new Date().getTime() })); } build_popup(); }, error: function(response){ console.log(response); } }); } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "WJuUcEXlLW41XFEN9ypxjk4IvBGgDetTk1uI3OEfqjkyq7Xhd248w2xHpwRvgQrO", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
FAQs
To find the integral of tan square x, we can use the trigonometric identities such as tan x = sin x/cos x and 1 + tan2x = sec2x. Mathematically, we can write the integration of tan square x as ∫ tan2x dx = tan x - x + C, where ∫ is the symbol of integration and C is the integration constant.
What are the topics for calculus 2 and 3? ›
Calculus 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates. Calculus 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integrations, and second-order differential equations.
What are the methods of integration in calculus? ›
There are many methods of integration that we use but the most common ones are 5, namely Integration by Parts, Method of Integration Using Partial Fractions, Integration by Substitution Method, Integration by Decomposition, and Reverse Chain Rule.
What is the integral of tan x? ›
The integration of tan x is ln|sec x| + C (or) -ln|cos x| + C.
What is the formula for tan 2x? ›
The formula for tan^2x are: tan^2x = sec^2x - 1 ⇒ tan2x = sec2x - 1. tan^2x = sin^2x / cos^2x ⇒ tan2x = sin2x/cos2x. tan^2x = 1/cot^2x ⇒ tan2x = 1/cot2x.
What does tan 2x equal? ›
It can be expressed as tan 2x or as a ratio of sin 2x to cos 2x. Since the reciprocal of tan x is cot x, we can write tan 2x as the reciprocal of cot 2x, that is, tan 2x= 1 / cot 2x .
How to find the derivative of tan 2x? ›
Derivative of Tan 2x Formula
The formula for the derivative of tan 2x is: d(tan 2x)/dx = 2 sec2(2x) (tan 2x)' = 2 sec2(2x)
How do you integrate a tan function? ›
Integration of Tan X
According to the definition of tan x, we have tan x equal to sin x divided by cos x. The substitution method of integration can be used to get the tan x indefinite integral. Hence the integration of tan x is ln|sec x| + C.
Is calculus 2 or 3 harder? ›
As for difficulty, it's quite subjective and depends on your strengths and what you find more challenging. Some students find Calc 2 tougher due to its heavy focus on integration techniques and series, whereas others may struggle more with Calc 3 as it involves more geometric and spatial reasoning.
What is the hardest math class? ›
What is the Hardest Math Class in High School? In most cases, you'll find that AP Calculus BC or IB Math HL is the most difficult math course your school offers. Note that AP Calculus BC covers the material in AP Calculus AB but also continues the curriculum, addressing more challenging and advanced concepts.
Calculus 2 is harder for a few reasons: There is no central theme. Calculus 1 is about differentiation, and integration, and ends with the fundamental theorem, unifying the two subjects. Calculus 3 is about studying calculus in higher dimensions, and generalizing the fundamental theorem over and over.
How to solve integrals easily? ›
Integration Using Trigonometric Identities
In the integration of a function, if the integrand involves any kind of trigonometric function, then we use trigonometric identities to simplify the function that can be easily integrated. All these identities simplify integrand, that can be easily found out.
How to learn integral calculus easily? ›
Below listed is a brief of a few fundamentals:
- Linearity. The integral is a linear operation. For any functions f(x) and g(x) and constants a and b, the following holds: ...
- Constant multiple. If C is a constant, then. ∫ c. ...
- Sum Rule. The integral of a sum is the sum of the integrals: ...
- Integration by parts. ∫ u dv = uv – ∫ v du.
In calculus, an integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus. Other words for integral include antiderivative and primitive.
What is the antiderivative of tan 2 x? ›
Hence, the antiderivative of tan 2 ( x ) d x is tan ( x ) - x + C , where is constant of integration.
What is the integration of tan inverse 2x dx? ›
The integral of tan-1 (2x) is x t a n − 1 ( 2 x ) − 1 4 l n ( 1 + 4 x 2 ) + C , where C is any constant. The formula for the integral of the inverse tangent function is as follows: ∫ t a n − 1 ( x ) d x = x t a n − 1 ( x ) − 1 2 l n ( 1 + x 2 ) + C , where C is any constant.
What is the derivative of tan 2x? ›
Mathematically, the derivative of tan 2x is written as d(tan 2x)/dx = 2 sec2(2x) or (tan 2x)' = 2 sec2(2x).
How do you integrate sin2 X? ›
Answer: The integration of sin square x is x/2 - (sin 2x)/4 + C. Go through the explanation to understand better. ☛Note: Here, ∫ cos 2x dx value can be computed using integration by substitution. where, C is the constant of integration.
