What is the integral of x^2*e^{x^2}*x ?

The integral of x^2*e^{x^2}*x is 1/2 e^{x^2}x^2-1/2 e^{x^2}+C

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integral of x^2e^{x^2}x

\int x^{2} \cdot e^{x^{2}} \cdot x d x

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

Solution steps

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

Apply Integration By Parts

: \frac{1}{2} e^{x^{2}} x^{2} - \int e^{x^{2}} x d x

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

Add a constant to the solution

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

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What is the integral of x^2*e^{x^2}*x ?
The integral of x^2*e^{x^2}*x is 1/2 e^{x^2}x^2-1/2 e^{x^2}+C