What is the integral of (t^2)/(e^t) ?

The integral of (t^2)/(e^t) is -(t^2)/(e^t)+2(-t/(e^t)-1/(e^t))+C

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integral of (t^2)/(e^t)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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