3.2398 \(\int (a+\frac{b}{\sqrt [3]{x}}) \, dx\)

Optimal. Leaf size=14 \[ a x+\frac{3}{2} b x^{2/3} \]

[Out]

(3*b*x^(2/3))/2 + a*x

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Rubi [A]  time = 0.0024813, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x+\frac{3}{2} b x^{2/3} \]

Antiderivative was successfully verified.

[In]

Int[a + b/x^(1/3),x]

[Out]

(3*b*x^(2/3))/2 + a*x

Rubi steps

\begin{align*} \int \left (a+\frac{b}{\sqrt [3]{x}}\right ) \, dx &=\frac{3}{2} b x^{2/3}+a x\\ \end{align*}

Mathematica [A]  time = 0.0013922, size = 14, normalized size = 1. \[ a x+\frac{3}{2} b x^{2/3} \]

Antiderivative was successfully verified.

[In]

Integrate[a + b/x^(1/3),x]

[Out]

(3*b*x^(2/3))/2 + a*x

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Maple [A]  time = 0., size = 11, normalized size = 0.8 \begin{align*}{\frac{3\,b}{2}{x}^{{\frac{2}{3}}}}+ax \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a+b/x^(1/3),x)

[Out]

3/2*b*x^(2/3)+a*x

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Maxima [A]  time = 0.954113, size = 14, normalized size = 1. \begin{align*} a x + \frac{3}{2} \, b x^{\frac{2}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x^(1/3),x, algorithm="maxima")

[Out]

a*x + 3/2*b*x^(2/3)

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Fricas [A]  time = 1.45375, size = 28, normalized size = 2. \begin{align*} a x + \frac{3}{2} \, b x^{\frac{2}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x^(1/3),x, algorithm="fricas")

[Out]

a*x + 3/2*b*x^(2/3)

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Sympy [A]  time = 0.052958, size = 12, normalized size = 0.86 \begin{align*} a x + \frac{3 b x^{\frac{2}{3}}}{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x**(1/3),x)

[Out]

a*x + 3*b*x**(2/3)/2

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Giac [A]  time = 1.19227, size = 14, normalized size = 1. \begin{align*} a x + \frac{3}{2} \, b x^{\frac{2}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x^(1/3),x, algorithm="giac")

[Out]

a*x + 3/2*b*x^(2/3)