Question #e4f3d

1 Answer
Jim H
Nov 13, 2016

There must be a typo. This integral cannot be done by substitution.

Explanation:

That 19x should (I assume) be 10x.

I = int((3x+5)dx)/(3x^2+10x+2)^(2/3)

Let u = 3x^2+10x+2. The du = (6x+10) dx = 2(3x+5) dx

I = 1/2 int(2(3x+5)dx)/(3x^2+10x+2)^(2/3)

= 1/2 int (du)/u^(2/3) = 1/2 int u^(-2/3) du = 1/2 (3u^1/3) +C

= 3/2 (3x^2+10x+2)^1/3 +C

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