How do you integrate #(x^3)(e^(x^2))dx#?

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Apr 7, 2017

Answer:

#1/2(x^2e^(x^2) - e^(x^2)) + C#

Explanation:

Use substitution method by considering #x^2 =u#, so that it is #x\ dx= 1/2\ du#.

The given integral is thus transformed to #1/2ue^u\ du#. Now integrate it by parts to have #1/2(ue^u-e^u) +C#.

Now substitute back #x^2# for u, to have the Integral as

#1/2(x^2e^(x^2) - e^(x^2)) + C#

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