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

  • #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.

Homework Statement



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

Homework Equations



Trigonometric substitutions, integration by parts maybe?

The Attempt at a Solution



This is a solved problem.

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How does [itex]\int\frac{x^{2}}{(xsinx+cosx)^{2}} dx[/itex] become [itex]\int xsecx \frac{xcosx}{(xsinx+cosx)^{2}} dx[/itex]?
 

Answers and Replies

  • #2
722
24
Just because [tex]sec(x)=\frac{1}{cos(x)}[/tex]
 
  • #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?
 
  • #4
SammyS
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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?
Yes.

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

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