Optimal. Leaf size=33 \[ \frac{3}{2} (x+1)^{2/3}-3 \sqrt [3]{x+1}+3 \log \left (\sqrt [3]{x+1}+1\right ) \]
[Out]
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Rubi [A] time = 0.0267663, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ \frac{3}{2} (x+1)^{2/3}-3 \sqrt [3]{x+1}+3 \log \left (\sqrt [3]{x+1}+1\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 + (1 + x)^(1/3))^(-1),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 3 \sqrt [3]{x + 1} + 3 \log{\left (\sqrt [3]{x + 1} + 1 \right )} + 3 \int ^{\sqrt [3]{x + 1}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+(1+x)**(1/3)),x)
[Out]
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Mathematica [A] time = 0.0116135, size = 33, normalized size = 1. \[ \frac{3}{2} (x+1)^{2/3}-3 \sqrt [3]{x+1}+3 \log \left (\sqrt [3]{x+1}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + (1 + x)^(1/3))^(-1),x]
[Out]
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Maple [A] time = 0.007, size = 47, normalized size = 1.4 \[ \ln \left ( 2+x \right ) +{\frac{3}{2} \left ( 1+x \right ) ^{{\frac{2}{3}}}}+2\,\ln \left ( 1+\sqrt [3]{1+x} \right ) -\ln \left ( \left ( 1+x \right ) ^{{\frac{2}{3}}}-\sqrt [3]{1+x}+1 \right ) -3\,\sqrt [3]{1+x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+(1+x)^(1/3)),x)
[Out]
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Maxima [A] time = 1.32782, size = 34, normalized size = 1.03 \[ \frac{3}{2} \,{\left (x + 1\right )}^{\frac{2}{3}} - 3 \,{\left (x + 1\right )}^{\frac{1}{3}} + 3 \, \log \left ({\left (x + 1\right )}^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 1)^(1/3) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212089, size = 34, normalized size = 1.03 \[ \frac{3}{2} \,{\left (x + 1\right )}^{\frac{2}{3}} - 3 \,{\left (x + 1\right )}^{\frac{1}{3}} + 3 \, \log \left ({\left (x + 1\right )}^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 1)^(1/3) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.131618, size = 29, normalized size = 0.88 \[ \frac{3 \left (x + 1\right )^{\frac{2}{3}}}{2} - 3 \sqrt [3]{x + 1} + 3 \log{\left (\sqrt [3]{x + 1} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+(1+x)**(1/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.210932, size = 34, normalized size = 1.03 \[ \frac{3}{2} \,{\left (x + 1\right )}^{\frac{2}{3}} - 3 \,{\left (x + 1\right )}^{\frac{1}{3}} + 3 \,{\rm ln}\left ({\left (x + 1\right )}^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 1)^(1/3) + 1),x, algorithm="giac")
[Out]