# Thread: integral with e^x (substitution rule)

1. ## integral with e^x (substitution rule)

I solved the following indefinite integral but my calculator tells me a different answer than what I got.

integral from ln4 to ln7 of e^x/(e^x-3)^2 dx

I set u=e^x -3 and du=e^x dx my new integral read:
integral from ln4 to ln7 of 1/u^2 du. My answer was u^-1 from ln4 to ln7 (1/e^x -3) I plugged in bounds and I got a value of -3/4.

I can't find my mistake

2. Originally Posted by swimmergirl
I solved the following indefinite integral but my calculator tells me a different answer than what I got.

integral from ln4 to ln7 of e^x/(e^x-3)^2 dx

I set u=e^x -3 and du=e^x dx my new integral read:
integral from ln4 to ln7 of 1/u^2 du. My answer was u^-1 from ln4 to ln7 (1/e^x -3) I plugged in bounds and I got a value of -3/4.

I can't find my mistake
$\int u^{-2}~du = {\color{red}-}u^{-1} + C$