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# Find the integral $\int n\left(2x\right)^2dx$

## Step-by-step Solution

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acosh
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###  Videos

$\frac{4x^{3}n}{3}+C_0$
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##  Step-by-step Solution 

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The integral of a function times a constant ($n$) is equal to the constant times the integral of the function

$n\int\left(2x\right)^2dx$

Learn how to solve integral calculus problems step by step online.

$n\int\left(2x\right)^2dx$

Learn how to solve integral calculus problems step by step online. Find the integral int(n(2x)^2)dx. The integral of a function times a constant (n) is equal to the constant times the integral of the function. The power of a product is equal to the product of it's factors raised to the same power. The integral of a function times a constant (4) is equal to the constant times the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as 2.

$\frac{4x^{3}n}{3}+C_0$

##  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 n2x^2dx using partial fractionsSolve integral of n2x^2dx using basic integralsSolve integral of n2x^2dx using u-substitutionSolve integral of n2x^2dx using integration by partsSolve integral of n2x^2dx using trigonometric substitution

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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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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