Integrating Rational Functions: Solving ∫(x/(x-1)^3)

[whatlifeforme]

Homework Statement

integrate the following:

Homework Equations

∫(x/(x-1)^3

The Attempt at a Solution

i've tried u-substitution, finding an inverse trig function that matched the formula, and still can't figure out how to solve this problem.

u-subtitution for u=x gives the same problem. u-subsitution for x-1 gives du =1 which does not match the problem.

 

[Dick]

Homework Statement

integrate the following:

Homework Equations

∫(x/(x-1)^3

The Attempt at a Solution

i've tried u-substitution, finding an inverse trig function that matched the formula, and still can't figure out how to solve this problem.

u-subtitution for u=x gives the same problem. u-subsitution for x-1 gives du =1 which does not match the problem.

u=(x-1) gives du=dx which does match the problem. If you are worried about the x in the numerator, if u=x-1, then x=u+1.

 

[Hysteria X]

Its a fairly easy integral..dont go all complicated when you can't find the answer just stay on the ground bro sometimes few problems can be easily solved if you just view it from a different angle

u=x-1, then x=u+1.

this should work. you would get u+1/u^3 du which you split and integrate

 

[Ray Vickson]

Its a fairly easy integral..dont go all complicated when you can't find the answer just stay on the ground bro sometimes few problems can be easily solved if you just view it from a different angle



this should work. you would get u+1/u^3 du which you split and integrate

No, you will not get $$u + \frac{1}{u^3},$$ which is what you wrote! If you really mean $$\frac{u+1}{u^3},$$ use parentheses, like this: (u+1)/u^3.

 

[Dick]

this should work. you would get u+1/u^3 du which you split and integrate

Good advice but use more parentheses. You could easily mistake u+1/u^3 for u+(1/u^3) when you meant (u+1)/u^3.

 

[Hysteria X]

No, you will not get $$u + \frac{1}{u^3},$$ which is what you wrote! If you really mean $$\frac{u+1}{u^3},$$ use parentheses, like this: (u+1)/u^3.

lol thanks for pointing it out..my bad :shy: