What is the integral of xe^{x^2}(1+x^2) ?

The integral of xe^{x^2}(1+x^2) is 1/2 e^{x^2}x^2+C

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integral of xe^{x^2}(1+x^2)

\int x e^{x^{2}} (1 + x^{2}) d x

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

Solution steps

\int x e^{x^{2}} (1 + x^{2}) d x

Apply Integration By Parts

= \frac{1}{2} e^{x^{2}} (1 + x^{2}) - \int e^{x^{2}} x d x

\int e^{x^{2}} x d x = \frac{1}{2} e^{x^{2}}

= \frac{1}{2} e^{x^{2}} (1 + x^{2}) - \frac{1}{2} e^{x^{2}}

Simplify

\frac{1}{2} e^{x^{2}} (1 + x^{2}) - \frac{1}{2} e^{x^{2}} : \frac{1}{2} e^{x^{2}} x^{2}

= \frac{1}{2} e^{x^{2}} x^{2}

Add a constant to the solution

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

What is the integral of xe^{x^2}(1+x^2) ?
The integral of xe^{x^2}(1+x^2) is 1/2 e^{x^2}x^2+C