How do I go about integrating sin[x^(1/3)]dx?? I tried doing integration by parts and I'm going in circles.

Question

How do I go about integrating sin[x^(1/3)]dx??  I tried doing integration by parts and I'm going in circles.

drwls · Answer

let x^(1/3) = w
w^3 = x
dx = 3w^2 dw
The integral becomes
3 *INTEGRAL w^2 sin w dw
The integral of that is in my table of integrals and it looks like you need to apply integration by parts twice to get it.

Hannah · Answer

I GOT IT! Thank you so so much for guiding me in the right direction!!

drwls · Answer

I'm sure glad you had the satisfaction of solving it; I was just too lazy to do the whole thing.