Optimal. Leaf size=22 \[ \frac{\log (x)}{a}-\frac{3 \log \left (a+b \sqrt [3]{x}\right )}{a} \]
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Rubi [A] time = 0.0315545, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ \frac{\log (x)}{a}-\frac{3 \log \left (a+b \sqrt [3]{x}\right )}{a} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x^(1/3))*x),x]
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Rubi in Sympy [A] time = 6.58708, size = 22, normalized size = 1. \[ \frac{3 \log{\left (\sqrt [3]{x} \right )}}{a} - \frac{3 \log{\left (a + b \sqrt [3]{x} \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b*x**(1/3))/x,x)
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Mathematica [A] time = 0.00800117, size = 27, normalized size = 1.23 \[ \frac{3 \log \left (\sqrt [3]{x}\right )}{a}-\frac{3 \log \left (a+b \sqrt [3]{x}\right )}{a} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x^(1/3))*x),x]
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Maple [A] time = 0.003, size = 21, normalized size = 1. \[ -3\,{\frac{\ln \left ( a+b\sqrt [3]{x} \right ) }{a}}+{\frac{\ln \left ( x \right ) }{a}} \]
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 = 1.44184, size = 27, normalized size = 1.23 \[ -\frac{3 \, \log \left (b x^{\frac{1}{3}} + a\right )}{a} + \frac{\log \left (x\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^(1/3) + a)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22336, size = 27, normalized size = 1.23 \[ -\frac{3 \,{\left (\log \left (b x^{\frac{1}{3}} + a\right ) - \log \left (x^{\frac{1}{3}}\right )\right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^(1/3) + a)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.60658, size = 37, normalized size = 1.68 \[ \begin{cases} \frac{\tilde{\infty }}{\sqrt [3]{x}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\log{\left (x \right )}}{a} & \text{for}\: b = 0 \\- \frac{3}{b \sqrt [3]{x}} & \text{for}\: a = 0 \\\frac{\log{\left (x \right )}}{a} - \frac{3 \log{\left (\frac{a}{b} + \sqrt [3]{x} \right )}}{a} & \text{otherwise} \end{cases} \]
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 = 0.21826, size = 30, normalized size = 1.36 \[ -\frac{3 \,{\rm ln}\left ({\left | b x^{\frac{1}{3}} + a \right |}\right )}{a} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^(1/3) + a)*x),x, algorithm="giac")
[Out]