Integrating \frac{x^3}{(x+1)^8}: Tips & Hints

[bob1182006]

Homework Statement

$$\int\frac{x^3 dx}{(x+1)^8}$$

Homework Equations

None I can think of.

The Attempt at a Solution

Hm..I just don't know where to start.

No substitution seems to be useful. (u=x+1, u=(x+1)^8).
I've tried pulling x out of the denominator to get:
$$\int\frac{x^3 dx}{x^8 (1+x^-1)^8}$$
but that doesn't help either..

This isn't really HW just one of 15 integrals I was given that I should be able to do...

Thanks in Advance for any hints on solving this.

 

[rocomath]

Homework Statement

$$\int\frac{x^3 dx}{(x+1)^8}$$

Homework Equations

None I can think of.

The Attempt at a Solution

Hm..I just don't know where to start.

No substitution seems to be useful. (u=x+1, u=(x+1)^8).
I've tried pulling x out of the denominator to get:
$$\int\frac{x^3 dx}{x^8 (1+x^-1)^8}$$
but that doesn't help either..

This isn't really HW just one of 15 integrals I was given that I should be able to do...

Thanks in Advance for any hints on solving this.

Cal 2? b/c i can't even go at it, I've only completed Cal 1.

 

[bob1182006]

Yep, Calc 2.

I "think" I could do partial fractions but...8 variables to find? and then 8 integrals of increasing power on the denominator. I think there should be an easier way...

 

[rocomath]

Yep, Calc 2.

I "think" I could do partial fractions but...8 variables to find? and then 8 integrals of increasing power on the denominator. I think there should be an easier way...

man i can't wait to be able to solve these types of problems :-]

i've missed it so much that i even did the even problems that weren't assigned for hw

 

[Dick]

u=x+1 is fine. Turns it into (u-1)^3/u^8. Now you just have to expand (u-1)^3. And if that's the worst of your 15 problems, feel blessed. It's really a calc 1 problem.

 

[bob1182006]

Wow thanks, this is about the 2nd time I've ever seen that type of substitution being used >.<.

Yea the problem's weren't really hard Calc 2 stuff mainly things we should know off the top of our heads.