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

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

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integral of t^{-2}e^t

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

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

Solution steps

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

Simplify

t^{- 2} e^{t} : \frac{e ^{t}}{t ^{2}}

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

Apply Integration By Parts

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

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

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

= - \frac{e ^{t}}{t} - (- Ei (t))

Simplify

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

Add a constant to the solution

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

(- 5, 2), (5, - 4)

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ln (1 + 4^{x})

\frac{d y}{d x} = x^{7} - \frac{1}{x ^{7}}

\frac{d}{d x} (3 + 4 x^{2} + 9 x^{4})

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