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

Step-by-step Solution

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Solution

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Final Answer

$\frac{3\sqrt[3]{4}}{2}\sqrt[3]{x^{2}}+C_0$
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Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

Simplify the expression inside the integral

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

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

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

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Unlock the first 2 steps of this solution.

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[3]{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.

Final Answer

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

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

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0
a
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n
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x
y
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(◻)
+
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×
◻/◻
/
÷
◻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:

Integrals of Rational Functions

Used formulas:

1. See formulas

Time to solve it:

~ 0.02 s

Related topics:

Integrals of Rational FunctionsIntegral CalculusCalculusIndefinite IntegralsIntegrals of Polynomial Functions

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