Question

What is the integral of `cos(x) / sqrt(1+sin^2(x)`?

Answer 1

`ln|sinx+sqrt(1+sin^2x)|+C.`

Explanation:

Let `I=int{cosx/sqrt(1+sin^2x)}dx`

Substitute `sinx = t,` so that, `cosxdx=dt.`

Hence, `I=int1/sqrt(1+t^2)dt=ln|t+sqrt(1+t^2|`, or,

`I=ln|sinx+sqrt(1+sin^2x)|+C.`