How do you find the integral of $e^(2x) sqrt(1 + e^(2x)) dx$ ?

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Answer 1 · 2015-06-09T10:36:04

$1/3 (1+e^(2x))^(3/2)$ +C

Let u= $1+e^(2x)$ , du= 2 $e^(2x)$ dx

Accordingly, $int e^(2x) sqrt(1+e^(2x) dx$ = $1/2int u^(1/2) du$

= $1/3 u^(3/2)$ +C

= $1/3 (1+e^(2x))^(3/2)$ +C

How do you find the integral of e^(2x) sqrt(1 + e^(2x)) dxe^(2x) sqrt(1 + e^(2x)) dx?