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

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Solution

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Final Answer

$\frac{3}{8}\sqrt[3]{x^{8}}+\frac{3}{2}\sqrt[3]{x^{2}}+C_0$
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Step-by-step Solution

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Expand the fraction $\frac{x^2+1}{\sqrt[3]{x}}$ into $2$ simpler fractions with common denominator $\sqrt[3]{x}$

$\int\left(\frac{x^2}{\sqrt[3]{x}}+\frac{1}{\sqrt[3]{x}}\right)dx$

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

$\int\left(\frac{x^2}{\sqrt[3]{x}}+\frac{1}{\sqrt[3]{x}}\right)dx$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2+1)/(x^1/3))dx. Expand the fraction \frac{x^2+1}{\sqrt[3]{x}} into 2 simpler fractions with common denominator \sqrt[3]{x}. Simplify the resulting fractions. Expand the integral \int\left(\sqrt[3]{x^{5}}+\frac{1}{\sqrt[3]{x}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sqrt[3]{x^{5}}dx results in: \frac{3}{8}\sqrt[3]{x^{8}}.

Final Answer

$\frac{3}{8}\sqrt[3]{x^{8}}+\frac{3}{2}\sqrt[3]{x^{2}}+C_0$

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 integral of ((x^2+1)/(x^0.3333))dx using partial fractionsSolve integral of ((x^2+1)/(x^0.3333))dx using basic integralsSolve integral of ((x^2+1)/(x^0.3333))dx using u-substitutionSolve integral of ((x^2+1)/(x^0.3333))dx using integration by partsSolve integral of ((x^2+1)/(x^0.3333))dx using trigonometric substitution

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Function Plot

Plotting: $\frac{3}{8}\sqrt[3]{x^{8}}+\frac{3}{2}\sqrt[3]{x^{2}}+C_0$

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a
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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

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Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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