MHB Integral of $\frac{1}{(3+4\sin x)^2}dx$

[juantheron]

$\displaystyle \int\frac{1}{(3+4\sin x)^2}dx$

 

[chisigma]

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]

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