# Math virtual assistant

Calculators Topics Go Premium About Snapxam

# Step-by-step Solution

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## 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 $-2x+-1$

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

The integral of the sum of two or more functions is equal to the sum of their integrals

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

## 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

~ 0.12 seconds