What is the integral of e^tt^2 ?

The integral of e^tt^2 is t^2e^t-2(e^tt-e^t)+C

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integral of e^tt^2

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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