How do you find the antiderivative of $cos (x) sin (sin (x)) d x$ $cos(x)sin(sin(x))dx$ ?

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Answer 1 · 2016-11-03T14:21:59

Substitute $u = sin x$ $u = sinx$

$\int sin (sin (x)) cos (x) d x$ $int sin(sin(x))cos(x) dx$

Let $u = sin x$ $u = sinx$ , then $d u = cos x d x$ $du = cosx dx$ , so the integral becomes

$\int sin u d u = - cos u + C$ $int sinu du = -cosu +C$

Reverse the substitution to finish

$= - cos (sin (x)) + C$ $= -cos(sin(x)) +C$

How do you find the antiderivative of cos(x)sin(sin(x))dxcos(x)sin(sin(x))dx?