What is the integral of $\int cos (x) sin (sin (x)) d x$ $int cos(x)sin(sin(x))dx$ ?

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Answer 1 · 2016-02-06T17:09:52

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

To begin, start by considering the substitution: $u = sin (x)$ $u = sin(x)$

So we also have that: $d u = cos (x) d x$ $du = cos(x)dx$

Substituting that into the integral will give:

$\int cos (x) sin (sin (x)) d x = \int sin (u) d u$ $intcos(x)sin(sin(x))dx = intsin(u)du$

We can now integrate to obtain:

$= - cos (u) + C$ $=-cos(u) + C$

And reversing the substitution we are left with:

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

What is the integral of int cos(x)sin(sin(x))dx∫cos(x)sin(sin(x))dxint cos(x)sin(sin(x))dx?