Integral problem??

Question

Let me tell you that I've been working on this for some time (alot) without any luck and it's starting to piss me off. I think there is a combination of substitution and integration by parts for this problem:

integral( (x^5)cos(x^3) )

Answer 1

put x^3=t differentiating both sides,3x^2d(x)=d(t)
=1/3integral x^5cost / x^2
=1/3integral x^3cost
=1/3integral tcost
=1/3[tsint-integral{sint}]
=1/3[tsint+cost]
=1/3[x^3sinx^3 + cosx^3]

Answer 2

if you put x^3=z and remember x^5 = x^3*x^2

3x^2dx = dz so your integral becomes Int 1/3 (z*cosz) dz
Now integrate by parts starting with the integral of cosz