Integration- (Substitution Rule) Help

[jordan123]

Homework Statement

Alright heres the problem. Also it is a definite integral from A=0 and b = 1
$$\int (x^7)(x^4-1)^{1/3}$$

Any help is good.

 

[HallsofIvy]

Well, what have you tried? There is only one subsitution that would make any sense and that is u= x⁴- 1. What do you get if you try that substitution?

 

[jordan123]

A pretty obvious substitution to try is u= x⁴- 1. Then du= 4x³dx so you can separate that x⁷ into x⁴ x³, use the "x³ with dx (and never write an integral without the "dx") and then x⁴= u+ 1.
$$\int x^7(x^4-1)dx= \int (u+1)u^{\frac{1}{3}}du= \int (u^{\frac{4}{3}}+ u^{\frac{1}{3}}*du$$

Ok right, exactly. And the new a and b would become a = -1 and b = 0 correct?

 

[jordan123]

Thanks, I got it now!!1