# Math Help - integral by substitution

1. ## integral by substitution

use the substitution u = 2^x to find the exact value of

integral at the top it says 1 and at the bottom 0 then a fraction :
top bit = 2^x
bottom bit = (2^x = 1) squared
then in the middle at the end it says dx

2. Originally Posted by cvmsmaths
use the substitution u = 2^x to find the exact value of

integral at the top it says 1 and at the bottom 0 then a fraction :
top bit = 2^x
bottom bit = (2^x = 1) squared
then in the middle at the end it says dx
Do you mean $\int_{0}^1 \frac{2^x}{(2^x + 1)^2} \, dx$?
Well then do as it says. Sub $u = 2^x \Rightarrow du = 2^x \ln 2 \, dx$

Thus $\int_{0}^1 \frac{2^x}{(2^x + 1)^2} \, dx = \frac1{\ln2}\int_{1}^2 \frac1{(u + 1)^2} \, du$