Can substitution be used to find the indefinite integral of 2x/(x+5)^6?

[zzinfinity]

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!

 

[gb7nash]

Use u-substitution. What can you set u equal to?

 

[Mark44]

There's a very obvious substitution.

 

[zzinfinity]

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?

 

[Mark44]

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.

 

[zzinfinity]

Got it. Thanks!