Integral of exponential function

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$\int xe^{2x^{2}} \; dx$

**Answer**

$\int xe^{2x^{2}} \; dx$

Substitute $u= 2x^{2}$. So, $du = 4x\; dx$, or $x\;dx =\frac{1}{4}\; du $

Then $\int x e^{2x^{2}} \; dx$

$=\frac{1}{4}\int e^u \; du $

$=\frac{1}{4}e^u + C $

Substituting back $u=2x^{2}$

$=\frac{1}{4} e^{2x^{2}} + C$