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

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

[Out]

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

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Rubi [A]  time = 0.00884017, 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 \[ x \sqrt [3]{\frac{b}{x^3}} \log (x) \]

Antiderivative was successfully verified.

[In]  Int[(b/x^3)^(1/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.17914, size = 12, normalized size = 0.92 \[ x \sqrt [3]{\frac{b}{x^{3}}} \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00202677, size = 13, normalized size = 1. \[ x \sqrt [3]{\frac{b}{x^3}} \log (x) \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^3)^(1/3),x]

[Out]

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

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Maple [A]  time = 0.017, size = 12, normalized size = 0.9 \[ \sqrt [3]{{\frac{b}{{x}^{3}}}}x\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x^3)^(1/3),x)

[Out]

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

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Maxima [A]  time = 1.43394, size = 15, normalized size = 1.15 \[ x \left (\frac{b}{x^{3}}\right )^{\frac{1}{3}} \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.22838, size = 15, normalized size = 1.15 \[ x \left (\frac{b}{x^{3}}\right )^{\frac{1}{3}} \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((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. \[ \int \left (\frac{b}{x^{3}}\right )^{\frac{1}{3}}\,{d x} \]

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)