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Step-by-step Solution

Integrate $\int e^x\left(x^2-2x-1\right)dx$ with respect to x

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Answer

$e^x\left(4-4x\right)+e^x\cdot x^2-e^x+C_0$

Step-by-step explanation

Problem to solve:

$\int e^x\left(x^2\:-\:2x\:-1\right)dx$
1

Multiplying polynomials $e^x$ and $-2x+-1$

$\int\left(e^x\cdot x^2-2e^x\cdot x-e^x\right)dx$
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The integral of the sum of two or more functions is equal to the sum of their integrals

$\int e^x\cdot x^2dx+\int-2e^x\cdot xdx+\int-e^xdx$

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Answer

$e^x\left(4-4x\right)+e^x\cdot x^2-e^x+C_0$
$\int e^x\left(x^2\:-\:2x\:-1\right)dx$

Main topic:

Integration by parts

Related formulas:

5. See formulas

Time to solve it:

~ 0.12 seconds