Problem

$\int x^{3} e^{x^{2}} d x$

Answer

Expert–verified

Hide Steps

Answer

$\int x^{3} e^{x^{2}} d x = \int x^{3} e^{u} \frac{d u}{2 x}$

Steps

Step 1 ： $u = x^{2}$

Step 2 ： $d u = 2 x d x$ $\Rightarrow d x = \frac{d u}{2 x}$

Step 3 ： $\int x^{3} e^{x^{2}} d x = \int x^{3} e^{u} \frac{d u}{2 x}$

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