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Find the integral $\int\left(e^{2x}\right)^4dx$

Step-by-step Solution

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$\frac{1}{8}e^{8x}+C_0$
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Step-by-step Solution

Problem to solve:

$\int\left(e^{2x}\right)^4dx$

Specify the solving method

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Simplify $\left(e^{2x}\right)^4$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2x$ and $n$ equals $4$

$\int e^{8x}dx$

Learn how to solve integrals of exponential functions problems step by step online.

$\int e^{8x}dx$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(e^(2x)^4)dx. Simplify \left(e^{2x}\right)^4 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2x and n equals 4. We can solve the integral \int e^{8x}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 8x 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. Isolate dx in the previous equation.

$\frac{1}{8}e^{8x}+C_0$
SnapXam A2

beta Got another answer? Verify it!

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

$\int\left(e^{2x}\right)^4dx$