Optimal. Leaf size=15 \[ \frac{3 \log \left (a \sqrt [3]{x}+b\right )}{a} \]
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Rubi [A] time = 0.0231028, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{3 \log \left (a \sqrt [3]{x}+b\right )}{a} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^(1/3))*x),x]
[Out]
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Rubi in Sympy [A] time = 4.04181, size = 12, normalized size = 0.8 \[ \frac{3 \log{\left (a \sqrt [3]{x} + b \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**(1/3))/x,x)
[Out]
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Mathematica [A] time = 0.00711098, size = 15, normalized size = 1. \[ \frac{3 \log \left (a \sqrt [3]{x}+b\right )}{a} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^(1/3))*x),x]
[Out]
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Maple [A] time = 0.001, size = 14, normalized size = 0.9 \[ 3\,{\frac{\ln \left ( b+a\sqrt [3]{x} \right ) }{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^(1/3))/x,x)
[Out]
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Maxima [A] time = 1.41762, size = 27, normalized size = 1.8 \[ \frac{3 \, \log \left (a + \frac{b}{x^{\frac{1}{3}}}\right )}{a} + \frac{\log \left (x\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^(1/3))*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228615, size = 18, normalized size = 1.2 \[ \frac{3 \, \log \left (a x^{\frac{1}{3}} + b\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^(1/3))*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.35549, size = 20, normalized size = 1.33 \[ \begin{cases} \frac{3 \log{\left (\sqrt [3]{x} + \frac{b}{a} \right )}}{a} & \text{for}\: a \neq 0 \\\frac{3 \sqrt [3]{x}}{b} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**(1/3))/x,x)
[Out]
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GIAC/XCAS [A] time = 0.213621, size = 19, normalized size = 1.27 \[ \frac{3 \,{\rm ln}\left ({\left | a x^{\frac{1}{3}} + b \right |}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^(1/3))*x),x, algorithm="giac")
[Out]