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

Step-by-step Solution

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Solution

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Final Answer

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

Problem to solve:

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

Specify the solving method

1

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.

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

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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. Rewrite the expression \left(2x\right)^2 inside the integral in factored form. 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.

Final Answer

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

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 int(n(2x)^2)dx using partial fractionsSolve int(n(2x)^2)dx using basic integralsSolve int(n(2x)^2)dx using u-substitutionSolve int(n(2x)^2)dx using integration by partsSolve int(n(2x)^2)dx 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
D□x
∫
∫◻
|◻|
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

How to improve your answer:

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Main topic:

Integral Calculus

Used formulas:

2. See formulas

Time to solve it:

~ 0.05 s

Related topics:

Integral CalculusCalculusIntegrals of Polynomial Functions

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