How do you integrate $(e^(sqrt(1+3x)))dx$ ?

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Answer 1 · 2016-06-26T10:27:35

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

$int \ (e^(sqrt(1+3x))) \ dx$

sub $p = sqrt(1+3x), \qquad dp = 3/(2 sqrt(1+3x)) dx = 3/(2p) dx$

$\implies 2/3 int \ p e^p \ dp$

IBP

$u = p, u' = 1$
$v' = e^p, v = e^p$

$\implies 2/3 ( p e^p - int \ e^p \ dp)$

$= 2/3 ( p e^p - e^p ) + C$

$= 2/3 *e^p ( p - 1) + C$

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

How do you integrate (e^(sqrt(1+3x)))dx(e^(sqrt(1+3x)))dx?