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Step-by-step Solution

Integral of $\frac{2z}{e^z}$ with respect to x

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Answer

$\frac{-2z-2}{e^z}+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(\frac{2z}{e^z}\right)dz$
1

Taking the constant out of the integral

$2\int\frac{z}{e^z}dz$
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Rewrite the fraction $\frac{z}{e^z}$ inside the integral as a product $z\frac{1}{e^z}$

$2\int z\frac{1}{e^z}dz$

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Answer

$\frac{-2z-2}{e^z}+C_0$
$\int\left(\frac{2z}{e^z}\right)dz$

Main topic:

Integrals of Rational Functions

Used formulas:

2. See formulas

Time to solve it:

~ 0.85 seconds