I've searched online for an answer to this, but the answers I've found are full of (gamma?) notation that I don't understand and haven't yet been taught. I didn't think it should be that difficult, yet I can't figure out the answer.

Evaluate the integral of sin(x^3) dx

I know the antiderivative of sin is -cos, and the antiderivative of x^3 could be x^4 / 4 but I can't figure out how to make it work here.

I tried making u = x^3 so that the answer would be -cos u^2/2 but then is the answer -1/2cos(x^3)^2 ??

Surely I should have to integrate x^3, right?