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

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Answer 1 · 2016-07-11T13:50:41

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

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,

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

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