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

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Answer 1 · 2016-02-06T17:09:52

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

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

So we also have that: # du = cos(x)dx#

Substituting that into the integral will give:

#intcos(x)sin(sin(x))dx = intsin(u)du#

We can now integrate to obtain:

#=-cos(u) + C#

And reversing the substitution we are left with:

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