Try now NerdPal! Our new app on iOS and Android

# Integrate the function $e^{\left(x+8\right)}$ from $3$ to $4$

## Step-by-step Solution

Go!
Math mode
Text mode
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

###  Videos

$102880.649704$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

$\int_{3}^{4} e^{\left(x+8\right)}dx$

Specify the solving method

1

We can solve the integral $\int_{3}^{4} e^{\left(x+8\right)}dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. We see that $x+8$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

$u=x+8$

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

$u=x+8$

Learn how to solve definite integrals problems step by step online. Integrate the function e^(x+8) from 3 to 4. We can solve the integral \int_{3}^{4} e^{\left(x+8\right)}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+8 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Substituting u and dx in the integral and simplify. The integral of the exponential function is given by the following formula \displaystyle \int a^xdx=\frac{a^x}{\ln(a)}, where a > 0 and a \neq 1.

$102880.649704$

##  Explore different ways to solve this problem

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

~ 0.02 s

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account