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

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

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integral of t^2e^{(-t)}

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

x \to 2 lim (x^{3} + 2 x)

\frac{d}{d x} (ln (x^{2} + 1) + e^{- x^{2}})

\int csc (θ) cot (θ) d θ

x \to + 0 + lim ((tan (3 x)) x)

\int (sin^{2} (x)) (cos^{2} (x)) d x

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