Integrals... more darn integrals?

Question

int of
x sec^2(x^3) dx

Answer 1

i think you can solve this by part

∫xsec²(x³) dx
u =x , dv=sec²(x³)
↓------------↓
du =dx , v=tanx³

xtanx³ -∫tanx³ dx
xtanx³ -(-InIcosx³I)+c
xtanx³ +In Icosx³I+c

Answer 2

I did not find out the solution.
In any case the Inttan(x^3)dx is NOT - lncos(x^3) as the derivative of this function is
-1/cos(x^3) *(-sin x^3)*3x^2