What is the antiderivative of cos(x)sin(sin(x))dx?

1 Answer
Apr 19, 2016

-cos(sin(x))+C

Explanation:

We will want to make use of the following integral:

intsin(u)du=-cos(u)+C

Thus, we want to set the interior of the sin function, which is in fact another sin function, equal to u.

So, we want to set u=sin(x). This implies that (du)/dx=cos(x) and du=cos(x)dx.

Thus, we have

intcos(x)sin(sin(x))dx=intsin(sin(x))*cos(x)dx

=intsin(u)du=-cos(u)+C=-cos(sin(x))+C