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Integration of x^2/(xsinx+cosx)^2

  1. Mar 29, 2014 #1
    Hi everyone,

    First of all, this isn't really a "homework", I've completed my calculus course and I'm just curious about this problem.

    1. The problem statement, all variables and given/known data

    [itex]\int\frac{x^{2}}{(xsinx+cosx)^{2}} dx[/itex]

    2. Relevant equations

    Trigonometric substitutions, integration by parts maybe?

    3. The attempt at a solution

    This is a solved problem.

    iK9Z0GF.png

    How does [itex]\int\frac{x^{2}}{(xsinx+cosx)^{2}} dx[/itex] become [itex]\int xsecx \frac{xcosx}{(xsinx+cosx)^{2}} dx[/itex]?
     
  2. jcsd
  3. Mar 29, 2014 #2
    Just because [tex]sec(x)=\frac{1}{cos(x)}[/tex]
     
  4. Mar 29, 2014 #3
    Did it multiply the numerator and denominator by [itex]\frac{cosx}{cosx}[/itex], which is [itex]cosx secx[/itex], and then both of [itex]cosx[/itex] and [itex]secx[/itex] took one "x" from the original numerator?
     
  5. Mar 29, 2014 #4

    SammyS

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    Yes.

    In other words, ##\ \cos(x)\cdot\sec(x) = 1 \ .##
     
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