How do you evaluate the integral $int e^(2x)sqrt(1+e^(2x))$ ?

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Answer 1 · 2017-03-01T20:21:24

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

Let $u = 1 + e^(2x)$ . Then $du = 2e^(2x)dx$ and $dx = (du)/(2e^(2x))$ .

$int e^(2x)sqrt(u) * (du)/(2e^(2x))$

$1/2int sqrt(u) du$

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

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

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

Hopefully this helps!

How do you evaluate the integral int e^(2x)sqrt(1+e^(2x))int e^(2x)sqrt(1+e^(2x))?