How do you integrate ∫cos3(x3)dx?
1 Answer
Jan 9, 2017
Explanation:
First let
∫cos3(x3)dx=3∫cos3(x3)13dx=3∫cos3(t)dt
To do this, split up
3∫cos3(t)dt=3∫cos2(t)cos(t)dt=3∫(1−sin2(t))cos(t)dt
Now let
3∫(1−sin2(t))cos(t)dt=3∫(1−s2)ds
Integrating term by term using
3∫(1−s2)ds=3(s−s33)=3s−s3
From
3s−s3=3sin(x3)−sin3(x3)+C