Optimal. Leaf size=13 \[ a \log (x)-\frac{3 b}{\sqrt [3]{x}} \]
[Out]
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Rubi [A] time = 0.0148795, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ a \log (x)-\frac{3 b}{\sqrt [3]{x}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))/x,x]
[Out]
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Rubi in Sympy [A] time = 2.86631, size = 12, normalized size = 0.92 \[ a \log{\left (x \right )} - \frac{3 b}{\sqrt [3]{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))/x,x)
[Out]
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Mathematica [A] time = 0.0113008, size = 13, normalized size = 1. \[ a \log (x)-\frac{3 b}{\sqrt [3]{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))/x,x]
[Out]
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Maple [A] time = 0.009, size = 12, normalized size = 0.9 \[ -3\,{\frac{b}{\sqrt [3]{x}}}+a\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))/x,x)
[Out]
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Maxima [A] time = 1.42461, size = 15, normalized size = 1.15 \[ a \log \left (x\right ) - \frac{3 \, b}{x^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224472, size = 24, normalized size = 1.85 \[ \frac{3 \,{\left (a x^{\frac{1}{3}} \log \left (x^{\frac{1}{3}}\right ) - b\right )}}{x^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.56687, size = 12, normalized size = 0.92 \[ a \log{\left (x \right )} - \frac{3 b}{\sqrt [3]{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))/x,x)
[Out]
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GIAC/XCAS [A] time = 0.219377, size = 16, normalized size = 1.23 \[ a{\rm ln}\left ({\left | x \right |}\right ) - \frac{3 \, b}{x^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))/x,x, algorithm="giac")
[Out]