Integral of exponential function

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$\int xe^{-15x^{2}} \; dx$

**Answer**

$\int xe^{-15x^{2}} \; dx$

Substitute $u= -15x^{2}$. So, $du = -30x\; dx$, or $x\;dx =-\frac{1}{30}\; du $

Then $\int x e^{-15x^{2}} \; dx$

$=-\frac{1}{30}\int e^u \; du $

$=-\frac{1}{30}e^u + C $

Substituting back $u=-15x^{2}$

$=-\frac{1}{30} e^{-15x^{2}} + C$