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Integration Problem

  • #1

Homework Statement



[tex] \int {\frac{sin^{2}x}{1+sin^{2}x}dx}[/tex]

Homework Equations



Let t = tan x/2, then dx = 2/(1+t^2) and sin x = 2t / (1+t^2)

The Attempt at a Solution



I got up to the point where [tex] \int {\frac{8t^{2}}{(1+6t^{2}+t^{4})(1+t^{2})} dt}[/tex]. Not sure if I'm on the right track and if I am, do I use partial fractions after this?

The final answer is attached. Can't really make out the handwriting :/
 

Attachments

Last edited:

Answers and Replies

  • #2
1,860
0
Yes, it looks like partial fractions is the way to go after your substitution.
 
  • #3
Hmm after I do partial fractions, I get
[tex] \int {\frac{2}{1+t^{2}} + {\frac{-2t^{2}-2}{(1+6t^{2}+t^{4})} dt}[/tex]

After this, I do not know what's the next step. Kindly advise. Thanks.
 
  • #4
236
0
you are summing 2 functions of t , one of these two look very much like a derivative of a certain function..
 
  • #5
If you mean 2tan^-1 t, I can get this part. But what about the 2nd function?
 

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