trigonometric integration problem












1














Hello guys can someone please help me find the answer :




$$int sin x tan x~dx$$







indefinite-integrals







share|cite|improve this question





























    1














    Hello guys can someone please help me find the answer :




    $$int sin x tan x~dx$$







    indefinite-integrals







    share|cite|improve this question



























      1












      1








      1







      Hello guys can someone please help me find the answer :




      $$int sin x tan x~dx$$







      indefinite-integrals







      share|cite|improve this question















      Hello guys can someone please help me find the answer :




      $$int sin x tan x~dx$$







      indefinite-integrals




      indefinite-integrals






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited 41 mins ago









      mrtaurho

      3,1051930




      3,1051930










      asked 42 mins ago









      RS 2838484

      61




      61






















          2 Answers
          2






          active

          oldest

          votes


















          7














          Note that $$sin(x)tan(x)=frac{sin^2(x)}{cos(x)}=frac{1-cos^2(x)}{cos(x)}$$






          share|cite|improve this answer































            1














            Bioche's rules say you should make the substitution $;u=sin x$, $mathrm d u=cos x,mathrm dx$, so that
            $$int sin x tan x,mathrm dx=intfrac{sin^2x}{cos x},frac{mathrm du}{cos x}=intfrac{u^2}{1-u^2},mathrm du,$$
            the integral of a rational function. Thus it comes down to a decomposition into partial fractions.






            share|cite|improve this answer





















              Your Answer





              StackExchange.ifUsing("editor", function () {
              return StackExchange.using("mathjaxEditing", function () {
              StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
              StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
              });
              });
              }, "mathjax-editing");

              StackExchange.ready(function() {
              var channelOptions = {
              tags: "".split(" "),
              id: "69"
              };
              initTagRenderer("".split(" "), "".split(" "), channelOptions);

              StackExchange.using("externalEditor", function() {
              // Have to fire editor after snippets, if snippets enabled
              if (StackExchange.settings.snippets.snippetsEnabled) {
              StackExchange.using("snippets", function() {
              createEditor();
              });
              }
              else {
              createEditor();
              }
              });

              function createEditor() {
              StackExchange.prepareEditor({
              heartbeatType: 'answer',
              autoActivateHeartbeat: false,
              convertImagesToLinks: true,
              noModals: true,
              showLowRepImageUploadWarning: true,
              reputationToPostImages: 10,
              bindNavPrevention: true,
              postfix: "",
              imageUploader: {
              brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
              contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
              allowUrls: true
              },
              noCode: true, onDemand: true,
              discardSelector: ".discard-answer"
              ,immediatelyShowMarkdownHelp:true
              });


              }
              });














              draft saved

              draft discarded


















              StackExchange.ready(
              function () {
              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3049700%2ftrigonometric-integration-problem%23new-answer', 'question_page');
              }
              );

              Post as a guest















              Required, but never shown

























              2 Answers
              2






              active

              oldest

              votes








              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              7














              Note that $$sin(x)tan(x)=frac{sin^2(x)}{cos(x)}=frac{1-cos^2(x)}{cos(x)}$$






              share|cite|improve this answer




























                7














                Note that $$sin(x)tan(x)=frac{sin^2(x)}{cos(x)}=frac{1-cos^2(x)}{cos(x)}$$






                share|cite|improve this answer


























                  7












                  7








                  7






                  Note that $$sin(x)tan(x)=frac{sin^2(x)}{cos(x)}=frac{1-cos^2(x)}{cos(x)}$$






                  share|cite|improve this answer














                  Note that $$sin(x)tan(x)=frac{sin^2(x)}{cos(x)}=frac{1-cos^2(x)}{cos(x)}$$







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited 22 mins ago









                  Bernard

                  117k637111




                  117k637111










                  answered 38 mins ago









                  Dr. Sonnhard Graubner

                  72.6k32865




                  72.6k32865























                      1














                      Bioche's rules say you should make the substitution $;u=sin x$, $mathrm d u=cos x,mathrm dx$, so that
                      $$int sin x tan x,mathrm dx=intfrac{sin^2x}{cos x},frac{mathrm du}{cos x}=intfrac{u^2}{1-u^2},mathrm du,$$
                      the integral of a rational function. Thus it comes down to a decomposition into partial fractions.






                      share|cite|improve this answer


























                        1














                        Bioche's rules say you should make the substitution $;u=sin x$, $mathrm d u=cos x,mathrm dx$, so that
                        $$int sin x tan x,mathrm dx=intfrac{sin^2x}{cos x},frac{mathrm du}{cos x}=intfrac{u^2}{1-u^2},mathrm du,$$
                        the integral of a rational function. Thus it comes down to a decomposition into partial fractions.






                        share|cite|improve this answer
























                          1












                          1








                          1






                          Bioche's rules say you should make the substitution $;u=sin x$, $mathrm d u=cos x,mathrm dx$, so that
                          $$int sin x tan x,mathrm dx=intfrac{sin^2x}{cos x},frac{mathrm du}{cos x}=intfrac{u^2}{1-u^2},mathrm du,$$
                          the integral of a rational function. Thus it comes down to a decomposition into partial fractions.






                          share|cite|improve this answer












                          Bioche's rules say you should make the substitution $;u=sin x$, $mathrm d u=cos x,mathrm dx$, so that
                          $$int sin x tan x,mathrm dx=intfrac{sin^2x}{cos x},frac{mathrm du}{cos x}=intfrac{u^2}{1-u^2},mathrm du,$$
                          the integral of a rational function. Thus it comes down to a decomposition into partial fractions.







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered 13 mins ago









                          Bernard

                          117k637111




                          117k637111






























                              draft saved

                              draft discarded




















































                              Thanks for contributing an answer to Mathematics Stack Exchange!


                              • Please be sure to answer the question. Provide details and share your research!

                              But avoid …



                              • Asking for help, clarification, or responding to other answers.

                              • Making statements based on opinion; back them up with references or personal experience.


                              Use MathJax to format equations. MathJax reference.


                              To learn more, see our tips on writing great answers.





                              Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                              Please pay close attention to the following guidance:


                              • Please be sure to answer the question. Provide details and share your research!

                              But avoid …



                              • Asking for help, clarification, or responding to other answers.

                              • Making statements based on opinion; back them up with references or personal experience.


                              To learn more, see our tips on writing great answers.




                              draft saved


                              draft discarded














                              StackExchange.ready(
                              function () {
                              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3049700%2ftrigonometric-integration-problem%23new-answer', 'question_page');
                              }
                              );

                              Post as a guest















                              Required, but never shown





















































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown

































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown







                              -

                              Popular posts from this blog

                              A CLEAN and SIMPLE way to add appendices to Table of Contents and bookmarks

                              Image
                              0 I found a lot of questions abount appendices and ToC. Many users want appendices to be grouped in an Appendix part, however some problems arise with ToC, hyperref, PDF viewer bookmarks, and so on. There are different solutions which require extra packages, command patching and other extra code, however none of them satisfies me. I almost found an easy way to accomplish a good result, where appendices are added to bookmarks in the right way and hyperref links point to the right page. However, the number of the "Appendix" part page is wrong (it's the number of appendix A). Is there any EASY way to fix that? This is a MWE: documentclass{book} usepackage[nottoc,notlot,notlof]{tocbibind} usepackage{hyperref} begin{document} frontmatter tableofcontents mainmatter part{First} chapter{
                              Read more

                              Calculate evaluation metrics using cross_val_predict sklearn

                              Image
                              1 In the sklearn.model_selection.cross_val_predict page it is stated: Generate cross-validated estimates for each input data point. It is not appropriate to pass these predictions into an evaluation metric. Can someone explain what does it mean? If this gives estimate of Y (y prediction) for every Y (true Y), why can't I calculate metrics such as RMSE or coefficient of determination using these results? python scikit-learn cross-validation share | improve this question edited Nov 28 '18 at 17:52 desertnaut 20.3k 7 43 79
                              Read more

                              Insert data from modal to MySQL (multiple modal on website)

                              Image
                              0 I have problem with inserting data to MySQL from modal. My modal: <a href="#" class="badge badge-pill badge-success">6 komentarzy</a> <a href="#" class="badge badge-pill badge-danger">brak komentarzy</a> <a data-toggle="modal" href="#add_desk_comm_{$desk_['desk_id']}" data-target="#add_desk_comm_{$desk_['desk_id']}" class="ediiit">(dodaj)</a> <div class="modal fade" id="add_desk_comm_{$desk_['desk_id']}" tabindex="-1" role="dialog" aria-labelledby="edit_printer" aria-hidden="true"> <div class="modal-dialog" role="document">
                              Read more