How do you integrate $int xe^(x^2)$ using substitution?

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Answer 1 · 2016-09-23T13:35:37

Use substitution.

Let $u = x^2$ . This make $du = 2x dx$

$int xe^(x^2) dx = 1/2 int underbrace((e^(x^2)))_(e^u) underbrace(2xdx)_(du)$

So we have

$int xe^(x^2) dx = 1/2 int (e^(x^2)) 2xdx$

$= 1/2 int e^u du$

$= 1/2e^u +C$

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

(Check the answer by differentiating.)

How do you integrate int xe^(x^2)int xe^(x^2) using substitution?