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Evaluate integral of xe^(x^2) with respect to x

Evaluate integral of xe^(x^2) with respect to x
Let . Then , so . Rewrite using and .
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Let . Find .
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Differentiate .
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
Differentiate using the Exponential Rule which states that is where =.
Replace all occurrences of with .
Differentiate using the Power Rule which states that is where .
Move to the left of .
Reorder and .
Reorder and .
Rewrite the problem using and .
Since is constant with respect to , move out of the integral.
Replace all occurrences of with .
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