What is the integral of xe^(x^2)?

integral of xe^(x^2)

The integral of

xe^{x^2}

\frac{1}{2}e^{x^2} + C

.

Solution. We want to determine the integral of

xe^{x^2}

, i.e.:

\begin{align*} \int xe^{x^2}dx. \end{align*}

We will use the substitution method. Let

u = x^2

, then

du = 2x dx

. Therefore, we get:

\begin{align*} \int xe^{x^2}dx &= \frac{1}{2} \int e^u du \\ &= \frac{1}{2}e^u + C \\ &= \frac{1}{2}e^{x^2} + C. \end{align*}

Therefore, the integral of

xe^{x^2}

\frac{1}{2}e^{x^2} + C