Question

Integral of (x^5(x^6-8)^29)), let U=(x^6-8) and the answer must be in terms of x and not u.

Answer 1

int(x^5(x^6-8)^(29) \]

Answer 2

you are leaving out a dx in the integral, but differentiate u=x^6-8 to obtain du=6x^5 dx.
From this you can see that 1/6 du = x^5 dx, so the integral becomes
∫1/6u29du

now it is a simple matter of reversing the power rule. This integrates into 1/(6*30)u^30 +c
so all that is left is substituting back in for u
1/(180) (x^6-8)^30