help find integral of (2x+1)^(-2)?

Question

Please help find the integral of (2x+1)^(-2), Please explain how you got it. I got -(2x+1)^(-1) but Prof. said it is (-1/2)(2x+1)^(-1)
I used the rule: integral u^n = (u^(n+1))/(n+1)

Answer 1

Simple substitution. Define u as 2x+1 (which it seems you did). But, since you're integrating by dx, you have to change that too. What's du/dx, if u=2x+1? And given that, what can you replace dx with?

Answer 2

As you might expect, your professor is right. Make the substitution u=2x+1. then du/dx = 2; ∫(u^-2)*du*dx/du = ∫(u^-2)/2 du = 1/2 * ∫(u^-2)du. now you can use the rule you quoted, but there is a factor of 1/2 in front of the integral

Answer 3

^_^