Help me with this calc problem please

[duragezic]

Been doing these things the whole damn night last night and finally got them all done except for this one. We have to use the substitution rule to evaluate the integral. The original problem is:

(x^3+1)^(1/3) x^5

That's the cube root of the first quantity times the x to the fifth. Anyway, it seems no matter what I substitute for u, I always end up with two variables to integrate which I don't think is possible if it is respect to u and you got x's in there. ANy ideas?

 

[ngvepforever2]

Ok, let's see if I can help.

first

(x^3+1)=u and x^3=u-1
so
3x^2dx=du
dx=du/(3x^2)


take the 1/3 out from du/(3x^2)
now you have:
Integral of (1/3)( u^(1/3) x^5 (du/x^2))
So as you can see the x^5 ends up being x^3 after you simplify with the x^2.
so substitute x^3 with u-1

now you have the integral of (1/3)(u^(1/3) (u-1) du)

and from there I think you can do it by yourself

Well,this looked so much better in paper I hope you understand.

Good luck

 

[duragezic]

Alright, I think I got it now. Thanks. I hadn't realized you could substitute the x^3 with u-1, which is why I was ending up trying to integrate with the x^3 still there even though it was with respect to u.