How do you find the integral of $cos(x)/(5+sin^2(x))dx$ ?

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Answer 1 · 2018-03-10T18:40:03

Given: $int cos(x)/(5+sin^2(x))dx$

Let $u = sin(x)$ , then $du = cos(x)dx)$ :

$int cos(x)/(5+sin^2(x))dx = int 1/(5+u^2)du$

You should recognize the right side as the inverse tangent form:

$int cos(x)/(5+sin^2(x))dx = sqrt5/5tan^-1(u/sqrt5)+ C$

Reverse the substitution for u:

$int cos(x)/(5+sin^2(x))dx = sqrt5/5tan^-1(sin(x)/sqrt5)+ C$

How do you find the integral of cos(x)/(5+sin^2(x))dxcos(x)/(5+sin^2(x))dx?