Question

Integral of 1/(x+1)^2. This feels like it should be simple, but I can't put my finger on the answer...

Answer 1

What is your best shot on the problem ?

Answer 2

\(\large\color{black}{\displaystyle\int\limits_{~}^{~}\frac{1}{w^n}~dw=\int\limits_{~}^{~}w^{-n}dw=\frac{1}{-n+1}w^{-n+1}+C}\)

Answer 3

\(\large\color{black}{\displaystyle\int\limits_{~}^{~}\frac{1}{w^2}~dw=\int\limits_{~}^{~}w^{-2}dw=\frac{1}{-2+1}w^{-2+1}+C=-w^{-1}+C}\)

Answer 4

I was thinking of product ruling it with (x+1)^-2 as u and dx as dv... but it doesn't seem like that'll go anywhere. The natural log antiderivat thing might work, but I haven't done it with a denominator to a power before...

Answer 5

No, see what I wrote above?
Do you agree with what I wrote?

Answer 6

When (x+1) is your variable that makes no difference because dx would =du if you set u=x+1, and thus you can just treat x+1 as a single variable, or if you like you can perform that u sub anyway

Answer 7

pellet, you're right. Goddamn substitution. Thanks.

Answer 8

Anytime \(!\)