What is the integral of r^2e^r ?

The integral of r^2e^r is r^2e^r-2(e^rr-e^r)+C

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integral of r^2e^r

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

r^{2} e^{r} - 2 (e^{r} r - e^{r}) + C

Solution steps

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

Apply Integration By Parts

: r^{2} e^{r} - \int 2 r e^{r} d r

= r^{2} e^{r} - \int 2 r e^{r} d r

\int 2 r e^{r} d r = 2 (e^{r} r - e^{r})

= r^{2} e^{r} - 2 (e^{r} r - e^{r})

Add a constant to the solution

= r^{2} e^{r} - 2 (e^{r} r - e^{r}) + C

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