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# Integrate the function $e^{\ln\left(x\right)}$ from $e$ to 0

## Step-by-step Solution

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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

###  Videos

$-3.694528$
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##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

1

Simplify the expression inside the integral

$-\int_{0}^{e} xdx$

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

$-\int_{0}^{e} xdx$

Learn how to solve definite integrals problems step by step online. Integrate the function e^ln(x) from e to 0. Simplify the expression inside the integral. Applying the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, in this case n=1. Evaluate the definite integral. Simplify the expression inside the integral.

$-3.694528$

##  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 integral of (e^lnx)dx from e to 0 using basic integralsSolve integral of (e^lnx)dx from e to 0 using u-substitutionSolve integral of (e^lnx)dx from e to 0 using integration by parts

SnapXam A2

Go!
1
2
3
4
5
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

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