Calc1.58

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\int x^{2}e^{x}\,dx\,

Use integration by parts twice to get this to an integral for which we know the formula.

u=x^{2}\,

du=2x\,dx\,

dv=e^{x}\,dx\,

v=e^{x}\,

\int x^{2}e^{x}\,dx=x^{2}e^{x}-2\int xe^{x}\,dx\,

u=x\,

du=dx\,

dv=e^{x}\,dx\,

v=e^{x}\,

\int x^{2}e^{x}=x^{2}e^{x}-2\left[xe^{x}-\int e^{x}\,dx\right]=x^{2}e^{x}-2xe^{x}+2e^{x}+C\,


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