What is the integral of t^2e^{8t} ?

The integral of t^2e^{8t} is 1/8 e^{8t}t^2-1/256 (8e^{8t}t-e^{8t})+C

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integral of t^2e^{8t}

\int t^{2} e^{8 t} d t

\frac{1}{8} e^{8 t} t^{2} - \frac{1}{256} (8 e^{8 t} t - e^{8 t}) + C

Solution steps

\int t^{2} e^{8 t} d t

Apply Integration By Parts

: \frac{1}{8} e^{8 t} t^{2} - \int \frac{1}{4} e^{8 t} t d t

= \frac{1}{8} e^{8 t} t^{2} - \int \frac{1}{4} e^{8 t} t d t

\int \frac{1}{4} e^{8 t} t d t = \frac{1}{256} (8 e^{8 t} t - e^{8 t})

= \frac{1}{8} e^{8 t} t^{2} - \frac{1}{256} (8 e^{8 t} t - e^{8 t})

Add a constant to the solution

= \frac{1}{8} e^{8 t} t^{2} - \frac{1}{256} (8 e^{8 t} t - e^{8 t}) + C

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What is the integral of t^2e^{8t} ?
The integral of t^2e^{8t} is 1/8 e^{8t}t^2-1/256 (8e^{8t}t-e^{8t})+C