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Step-by-step Solution

Integral of $3e^x\cdot x$

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Answer

$3e^x\cdot x-3e^x+C_0$

Step-by-step explanation

Problem to solve:

$\int3\cdot e^x\cdot xdx$
1

Take the constant out of the integral

$3\int e^x\cdot xdx$
2

Use the integration by parts theorem to calculate the integral $\int e^x\cdot xdx$, using the following formula

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

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Answer

$3e^x\cdot x-3e^x+C_0$
$\int3\cdot e^x\cdot xdx$

Main topic:

Integration by parts

Used formulas:

3. See formulas

Time to solve it:

~ 0.81 seconds