What is the integral of t*1/(e^t) ?

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

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integral of t*1/(e^t)

\int t \cdot \frac{1}{e ^{t}} d t

- \frac{t}{e ^{t}} - \frac{1}{e ^{t}} + C

Solution steps

\int t \frac{1}{e ^{t}} d t

Simplify

t \frac{1}{e ^{t}} : \frac{t}{e ^{t}}

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

Apply Integration By Parts

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

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

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

= - \frac{t}{e ^{t}} - \frac{1}{e ^{t}}

Add a constant to the solution

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

\int (- 2 sec (x) tan (x) - 3 sec^{2} (x)) d x

5 t \cdot \frac{d y}{d t} + 3 y = t

\frac{d x}{d t} = \frac{( 2 t ^{2} + x ^{2} )}{t x}

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{x} sin (x)

\int_{0}^{\infty} 1 d x

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