Question

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

Answer 1

`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`