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# Integrate the function $x+e^x$ from 0 to $2$

## Step-by-step Solution

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e
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ln
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sin
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asin
acos
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Videos

$8.389056$
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##  Step-by-step Solution 

Problem to solve:

$\int_{0}^{2}\left(x+e^x\right)dx$

Specify the solving method

1

Expand the integral $\int_{0}^{2}\left(x+e^x\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int_{0}^{2} xdx+\int_{0}^{2} e^xdx$

Learn how to solve definite integrals problems step by step online.

$\int_{0}^{2} xdx+\int_{0}^{2} e^xdx$

Learn how to solve definite integrals problems step by step online. Integrate the function x+e^x from 0 to 2. Expand the integral \int_{0}^{2}\left(x+e^x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{2} xdx results in: 2. The integral \int_{0}^{2} e^xdx results in: 6.389056. Gather the results of all integrals.

$8.389056$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int(x+e^x)dx&0&2 using partial fractionsSolve int(x+e^x)dx&0&2 using basic integralsSolve int(x+e^x)dx&0&2 using u-substitutionSolve int(x+e^x)dx&0&2 using integration by partsSolve int(x+e^x)dx&0&2 using tabular integrationSolve int(x+e^x)dx&0&2 using trigonometric substitution

SnapXam A2

Go!
1
2
3
4
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6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

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

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main topic:

Definite Integrals

~ 0.04 s

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