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Step-by-step Solution

Integrate $e^{-st}t$ from $0$ to $1$

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Answer

$\frac{-t\left(-1+e^{-s}\right)}{s}$

Step-by-step explanation

Problem to solve:

$\int_0^1e^{-st}t\:dt$
1

The integral of a constant by a function is equal to the constant multiplied by the integral of the function

$t\int_{0}^{1} e^{-st}dt$
2

Solve the integral $\int_{0}^{1} e^{-st}dt$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=-st \\ du=-sdt\end{matrix}$

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Answer

$\frac{-t\left(-1+e^{-s}\right)}{s}$
$\int_0^1e^{-st}t\:dt$

Main topic:

Definite integrals

Related formulas:

5. See formulas

Time to solve it:

~ 0.13 seconds