Optimal. Leaf size=45 \[ \frac{5 x^{4/5}}{4}-\frac{5 x^{3/5}}{3}+\frac{5 x^{2/5}}{2}-5 \sqrt [5]{x}+5 \log \left (\sqrt [5]{x}+1\right ) \]
[Out]
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Rubi [A] time = 0.04009, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{5 x^{4/5}}{4}-\frac{5 x^{3/5}}{3}+\frac{5 x^{2/5}}{2}-5 \sqrt [5]{x}+5 \log \left (\sqrt [5]{x}+1\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 + x^(1/5))^(-1),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{5 x^{\frac{4}{5}}}{4} - \frac{5 x^{\frac{3}{5}}}{3} - 5 \sqrt [5]{x} + 5 \log{\left (\sqrt [5]{x} + 1 \right )} + 5 \int ^{\sqrt [5]{x}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+x**(1/5)),x)
[Out]
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Mathematica [A] time = 0.0160331, size = 45, normalized size = 1. \[ \frac{5 x^{4/5}}{4}-\frac{5 x^{3/5}}{3}+\frac{5 x^{2/5}}{2}-5 \sqrt [5]{x}+5 \log \left (\sqrt [5]{x}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^(1/5))^(-1),x]
[Out]
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Maple [B] time = 0.065, size = 79, normalized size = 1.8 \[ \ln \left ( 1+x \right ) +{\frac{5}{2}{x}^{{\frac{2}{5}}}}+4\,\ln \left ( 1+\sqrt [5]{x} \right ) -\ln \left ( -\sqrt [5]{x}\sqrt{5}+2\,{x}^{2/5}-\sqrt [5]{x}+2 \right ) -\ln \left ( \sqrt [5]{x}\sqrt{5}+2\,{x}^{2/5}-\sqrt [5]{x}+2 \right ) +{\frac{5}{4}{x}^{{\frac{4}{5}}}}-5\,\sqrt [5]{x}-{\frac{5}{3}{x}^{{\frac{3}{5}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+x^(1/5)),x)
[Out]
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Maxima [A] time = 1.44003, size = 57, normalized size = 1.27 \[ \frac{5}{4} \,{\left (x^{\frac{1}{5}} + 1\right )}^{4} - \frac{20}{3} \,{\left (x^{\frac{1}{5}} + 1\right )}^{3} + 15 \,{\left (x^{\frac{1}{5}} + 1\right )}^{2} - 20 \, x^{\frac{1}{5}} + 5 \, \log \left (x^{\frac{1}{5}} + 1\right ) - 20 \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^(1/5) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237965, size = 39, normalized size = 0.87 \[ \frac{5}{4} \, x^{\frac{4}{5}} - \frac{5}{3} \, x^{\frac{3}{5}} + \frac{5}{2} \, x^{\frac{2}{5}} - 5 \, x^{\frac{1}{5}} + 5 \, \log \left (x^{\frac{1}{5}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^(1/5) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 12.8416, size = 41, normalized size = 0.91 \[ \frac{5 x^{\frac{4}{5}}}{4} - \frac{5 x^{\frac{3}{5}}}{3} + \frac{5 x^{\frac{2}{5}}}{2} - 5 \sqrt [5]{x} + 5 \log{\left (\sqrt [5]{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+x**(1/5)),x)
[Out]
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GIAC/XCAS [A] time = 0.214154, size = 39, normalized size = 0.87 \[ \frac{5}{4} \, x^{\frac{4}{5}} - \frac{5}{3} \, x^{\frac{3}{5}} + \frac{5}{2} \, x^{\frac{2}{5}} - 5 \, x^{\frac{1}{5}} + 5 \,{\rm ln}\left (x^{\frac{1}{5}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^(1/5) + 1),x, algorithm="giac")
[Out]