What is the integral of t^2e^{t^2} ?

The integral of t^2e^{t^2} is 1/2 e^{t^2}t-(sqrt(pi))/4 \erfi(t)+C

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integral of t^2e^{t^2}

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

\frac{1}{2} e^{t^{2}} t - \frac{π}{4} erfi (t) + C

Solution steps

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

Simplify

t^{2} : tt

= \int tt e^{t^{2}} d t

Apply Integration By Parts

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

= \frac{1}{2} e^{t^{2}} t - \int \frac{1}{2} e^{t^{2}} d t

\int \frac{1}{2} e^{t^{2}} d t = \frac{π}{4} erfi (t)

= \frac{1}{2} e^{t^{2}} t - \frac{π}{4} erfi (t)

Add a constant to the solution

= \frac{1}{2} e^{t^{2}} t - \frac{π}{4} erfi (t) + C

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What is the integral of t^2e^{t^2} ?
The integral of t^2e^{t^2} is 1/2 e^{t^2}t-(sqrt(pi))/4 \erfi(t)+C