Optimal. Leaf size=16 \[ \frac{3}{4} \log \left (1-\left (x^2\right )^{2/3}\right ) \]
[Out]
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Rubi [A] time = 0.0953562, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ \frac{3}{4} \log \left (1-\left (x^2\right )^{2/3}\right ) \]
Antiderivative was successfully verified.
[In] Int[x/(x^2 - (x^2)^(1/3)),x]
[Out]
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Rubi in Sympy [A] time = 4.7208, size = 12, normalized size = 0.75 \[ \frac{3 \log{\left (- \left (x^{2}\right )^{\frac{2}{3}} + 1 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x**2-(x**2)**(1/3)),x)
[Out]
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Mathematica [A] time = 0.0129344, size = 14, normalized size = 0.88 \[ \frac{3}{4} \log \left (\left (x^2\right )^{2/3}-1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x/(x^2 - (x^2)^(1/3)),x]
[Out]
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Maple [B] time = 0.056, size = 70, normalized size = 4.4 \[{\frac{\ln \left ({x}^{2}-1 \right ) }{4}}+{\frac{\ln \left ({x}^{2}+1 \right ) }{4}}-{\frac{1}{4}\ln \left ( \left ({x}^{2} \right ) ^{{\frac{2}{3}}}+\sqrt [3]{{x}^{2}}+1 \right ) }+{\frac{1}{2}\ln \left ( \sqrt [3]{{x}^{2}}-1 \right ) }+{\frac{1}{2}\ln \left ( 1+\sqrt [3]{{x}^{2}} \right ) }-{\frac{1}{4}\ln \left ( \left ({x}^{2} \right ) ^{{\frac{2}{3}}}-\sqrt [3]{{x}^{2}}+1 \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x^2-(x^2)^(1/3)),x)
[Out]
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Maxima [A] time = 0.719974, size = 28, normalized size = 1.75 \[ \frac{3}{4} \, \log \left ({\left (x^{2}\right )}^{\frac{1}{3}} + 1\right ) + \frac{3}{4} \, \log \left ({\left (x^{2}\right )}^{\frac{1}{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^2 - (x^2)^(1/3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.266958, size = 43, normalized size = 2.69 \[ -3 \, \log \left (\frac{{\left (x^{2}\right )}^{\frac{1}{3}}}{x}\right ) + \frac{3}{4} \, \log \left (-\frac{x^{2} -{\left (x^{2}\right )}^{\frac{1}{3}}}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^2 - (x^2)^(1/3)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.584835, size = 19, normalized size = 1.19 \[ - \frac{\log{\left (x \right )}}{2} + \frac{3 \log{\left (x^{2} - \sqrt [3]{x^{2}} \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x**2-(x**2)**(1/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.266682, size = 22, normalized size = 1.38 \[ \frac{3}{4} \,{\rm ln}\left ({\left | \left (x{\rm sign}\left (x\right )\right )^{\frac{1}{3}} x{\rm sign}\left (x\right ) - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^2 - (x^2)^(1/3)),x, algorithm="giac")
[Out]