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Step-by-step Solution

Integral of $we^w$

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Answer

$e^w\left(-1+w\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int w e^wdw$
1

Use the integration by parts theorem to calculate the integral $\int we^wdw$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
2

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=w}\\ \displaystyle{du=dw}\end{matrix}$

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Answer

$e^w\left(-1+w\right)+C_0$
$\int w e^wdw$

Main topic:

Integration by parts

Used formulas:

2. See formulas

Time to solve it:

~ 0.79 seconds