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# Find the integral $\int\frac{2x^{-\frac{1}{3}}}{\sqrt{2}}dx$

## Step-by-step Solution

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###  Videos

$\frac{3\sqrt{4}}{2}\sqrt{x^{2}}+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\frac{2x^{-\frac{1}{3}}}{\sqrt{2}}dx$

Specify the solving method

1

Simplify the expression inside the integral

$\int\sqrt{4}x^{-\frac{1}{3}}dx$

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

$\int\sqrt{4}x^{-\frac{1}{3}}dx$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((2x^(-1/3))/(2^1/3))dx. Simplify the expression inside the integral. The integral of a function times a constant (\sqrt{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 -\frac{1}{3}. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

$\frac{3\sqrt{4}}{2}\sqrt{x^{2}}+C_0$

##  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((2x^(-1/3))/(2^1/3))dx using partial fractionsSolve int((2x^(-1/3))/(2^1/3))dx using basic integralsSolve int((2x^(-1/3))/(2^1/3))dx using u-substitutionSolve int((2x^(-1/3))/(2^1/3))dx using integration by partsSolve int((2x^(-1/3))/(2^1/3))dx using trigonometric substitution

SnapXam A2

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5
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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:

Integrals of Rational Functions

~ 0.02 s

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