How do you integrate $int xsqrt(2x+1)$ using substitution?

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Answer 1 · 2016-07-26T00:15:16

$= 1/10(2x+1)^(5/2) - 1/6(2x+1)^(3/2) + C$

Let $u = 2x+1 implies du = 2dx$

$implies x = (u-1)/2 and dx = (du)/2$

$int xsqrt(2x+1)dx = 1/4 int (u-1)u^(1/2)du$

$= 1/4int u^(3/2) - u^(1/2)du$

$=1/4[2/5u^(5/2) - 2/3u^(3/2)] + C$

$= 1/10(2x+1)^(5/2) - 1/6(2x+1)^(3/2) + C$

How do you integrate int xsqrt(2x+1)int xsqrt(2x+1) using substitution?