What is the integral of 4t^2e^t ?

The integral of 4t^2e^t is 4(t^2e^t-2(e^tt-e^t))+C

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integral of 4t^2e^t

\int 4 t^{2} e^{t} d t

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

Solution steps

\int 4 t^{2} e^{t} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int t^{2} e^{t} d t

Apply Integration By Parts

= 4 (t^{2} e^{t} - \int 2 t e^{t} d t)

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

= 4 (t^{2} e^{t} - 2 (e^{t} t - e^{t}))

Add a constant to the solution

= 4 (t^{2} e^{t} - 2 (e^{t} t - e^{t})) + C

What is the integral of 4t^2e^t ?
The integral of 4t^2e^t is 4(t^2e^t-2(e^tt-e^t))+C