How do you integrate $(x^{3}) (e^{x^{2}}) d x$ $(x^3)(e^(x^2))dx$ ?

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Answer 1 · 2015-04-12T17:48:55

$\frac{1}{2} (x^{2} e^{x^{2}} - e^{x^{2}}) + C$ $1/2(x^2e^(x^2) - e^(x^2)) + C$

Use substitution method by considering $x^{2} = u$ $x^2 =u$ , 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

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

How do you integrate (x^3)(e^(x^2))dx(x3)(ex2)dx(x^3)(e^(x^2))dx?