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definite Integral

jacks

Well-known member
Apr 5, 2012
226
$\displaystyle \int\frac{1}{(3+4\sin x)^2}dx$
 

chisigma

Well-known member
Feb 13, 2012
1,704
Re: defeinite Integral

$\displaystyle \int\frac{1}{(3+4\sin x)^2}dx$
The 'standard' substition for this type of integral is...

$\displaystyle t= \tan \frac{x}{2} \implies x=2\ \tan^{-1} t \implies dx= \frac{2}{1+t^{2}}\ dt \implies \sin x=\frac{2 t}{1+t^{2}} \implies \cos x= \frac{1-t^{2}}{1+t^{2}}$

Kind regards

$\chi$ $\sigma$
 

CaptainBlack

Well-known member
Jan 26, 2012
890
Re: defeinite Integral

$\displaystyle \int\frac{1}{(3+4\sin x)^2}dx$
definite/indefinite integral?

This does have an (indefinite) integral in terms of elementary functions, but it is not particularly simple (at least if you assume Wolfram Alpha has chosen a good approach to doing this, it starts with the substitution chisigma proposes in his post. Alpha will give you the steps as well as the final answer so you may as well ask the horses mouth itself)

CB