Question

i need a hint to solve this integral:
cos(x)/(25+4(sin^2(x))

Answer 1

Like this?\[\int\limits \frac{\cos x}{25+4\sin^2 x}dx\]

Answer 2

yes

Answer 3

ii have been trying to substitute, but i can't find the right way to do it

Answer 4

you should let u=2sin x Then (after the substitutions) it will be in the form:\[\int\limits \frac{1}{25+u^2}du\]

Answer 5

yes i did that but i don't know what so do after

Answer 6

Its something that you have to memorize after that. When you have an integral in the form:\[\int\limits \frac{1}{a^2+x^2}dx\]the answer turns out to be:\[\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)+C\]

Answer 7

oh i didn't know that. Thank you!