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Integration by substitution

  • Thread starter zzinfinity
  • Start date
  • #1
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Homework Statement


Find the indefinite integral by substitution.

∫2x/(x+5)^6 dx


Homework Equations





The Attempt at a Solution


I know how to do this using the method of partial fractions, but the book says to use substitution. Is there a way to just do a basic u-substitution with this integrand that I'm just not seeing? Or a way to solve without partial fractions? (we haven't gotten to partial fractions in my class so I feel like there must be some other way).

Thanks!
 

Answers and Replies

  • #2
gb7nash
Homework Helper
805
1
Use u-substitution. What can you set u equal to?
 
  • #3
33,265
4,965
There's a very obvious substitution.
 
  • #4
47
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haha, thanks guys. I feel like it is pretty obvious but I just don't see it! If you set u=x+5 that gives du=1dx and you're still stuck with the 2x in the numerator. If you set u=2x, you get du=2dx and then you're stuck with the (x+5)^6 in the denominator.

What am I missing????
 
  • #5
33,265
4,965
If u = x + 5, what is x in terms of u? When you do a substitution, you don't just replace some of the terms.
 
  • #6
47
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Got it. Thanks!
 

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