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Integration Help

  • Thread starter bob1182006
  • Start date
  • #1
492
1

Homework Statement


[tex]\int\frac{x^3 dx}{(x+1)^8}[/tex]


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:
[tex]\int\frac{x^3 dx}{x^8 (1+x^-1)^8}[/tex]
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.
 

Answers and Replies

  • #2
1,752
1

Homework Statement


[tex]\int\frac{x^3 dx}{(x+1)^8}[/tex]


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:
[tex]\int\frac{x^3 dx}{x^8 (1+x^-1)^8}[/tex]
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.
 
  • #3
492
1
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...
 
  • #4
1,752
1
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
 
  • #5
Dick
Science Advisor
Homework Helper
26,258
618
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.
 
Last edited:
  • #6
492
1
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.
 

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