3.118 \(\int \frac{1}{\sqrt [3]{b x^3}} \, dx\)

Optimal. Leaf size=13 \[ \frac{x \log (x)}{\sqrt [3]{b x^3}} \]

[Out]

(x*Log[x])/(b*x^3)^(1/3)

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Rubi [A]  time = 0.00639038, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{x \log (x)}{\sqrt [3]{b x^3}} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^3)^(-1/3),x]

[Out]

(x*Log[x])/(b*x^3)^(1/3)

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Rubi in Sympy [A]  time = 1.55394, size = 15, normalized size = 1.15 \[ \frac{\left (b x^{3}\right )^{\frac{2}{3}} \log{\left (x \right )}}{b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(b*x**3)**(1/3),x)

[Out]

(b*x**3)**(2/3)*log(x)/(b*x**2)

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Mathematica [A]  time = 0.00315503, size = 13, normalized size = 1. \[ \frac{x \log (x)}{\sqrt [3]{b x^3}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^3)^(-1/3),x]

[Out]

(x*Log[x])/(b*x^3)^(1/3)

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Maple [A]  time = 0.013, size = 12, normalized size = 0.9 \[{x\ln \left ( x \right ){\frac{1}{\sqrt [3]{b{x}^{3}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x^3)^(1/3),x)

[Out]

x*ln(x)/(b*x^3)^(1/3)

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Maxima [A]  time = 1.43088, size = 15, normalized size = 1.15 \[ \frac{x \log \left (x\right )}{\left (b x^{3}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3)^(-1/3),x, algorithm="maxima")

[Out]

x*log(x)/(b*x^3)^(1/3)

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Fricas [A]  time = 0.226334, size = 22, normalized size = 1.69 \[ \frac{\left (b x^{3}\right )^{\frac{2}{3}} \log \left (x\right )}{b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3)^(-1/3),x, algorithm="fricas")

[Out]

(b*x^3)^(2/3)*log(x)/(b*x^2)

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt [3]{b x^{3}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x**3)**(1/3),x)

[Out]

Integral((b*x**3)**(-1/3), x)

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (b x^{3}\right )^{\frac{1}{3}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3)^(-1/3),x, algorithm="giac")

[Out]

integrate((b*x^3)^(-1/3), x)