Optimal. Leaf size=41 \[ \frac{6 t^{7/6}}{7}-\frac{6 t^{5/6}}{5}+2 \sqrt{t}-6 \sqrt [6]{t}+6 \tan ^{-1}\left (\sqrt [6]{t}\right ) \]
[Out]
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Rubi [A] time = 0.033075, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ \frac{6 t^{7/6}}{7}-\frac{6 t^{5/6}}{5}+2 \sqrt{t}-6 \sqrt [6]{t}+6 \tan ^{-1}\left (\sqrt [6]{t}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[t]/(1 + t^(1/3)),t]
[Out]
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Rubi in Sympy [A] time = 2.71242, size = 37, normalized size = 0.9 \[ \frac{6 t^{\frac{7}{6}}}{7} - \frac{6 t^{\frac{5}{6}}}{5} - 6 \sqrt [6]{t} + 2 \sqrt{t} + 6 \operatorname{atan}{\left (\sqrt [6]{t} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(t**(1/2)/(1+t**(1/3)),t)
[Out]
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Mathematica [A] time = 0.0144812, size = 41, normalized size = 1. \[ \frac{6 t^{7/6}}{7}-\frac{6 t^{5/6}}{5}+2 \sqrt{t}-6 \sqrt [6]{t}+6 \tan ^{-1}\left (\sqrt [6]{t}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[t]/(1 + t^(1/3)),t]
[Out]
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Maple [A] time = 0.004, size = 28, normalized size = 0.7 \[ -6\,\sqrt [6]{t}-{\frac{6}{5}{t}^{{\frac{5}{6}}}}+{\frac{6}{7}{t}^{{\frac{7}{6}}}}+6\,\arctan \left ( \sqrt [6]{t} \right ) +2\,\sqrt{t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(t^(1/2)/(1+t^(1/3)),t)
[Out]
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Maxima [A] time = 1.49266, size = 36, normalized size = 0.88 \[ \frac{6}{7} \, t^{\frac{7}{6}} - \frac{6}{5} \, t^{\frac{5}{6}} + 2 \, \sqrt{t} - 6 \, t^{\frac{1}{6}} + 6 \, \arctan \left (t^{\frac{1}{6}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(t)/(t^(1/3) + 1),t, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215419, size = 34, normalized size = 0.83 \[ \frac{6}{7} \,{\left (t - 7\right )} t^{\frac{1}{6}} - \frac{6}{5} \, t^{\frac{5}{6}} + 2 \, \sqrt{t} + 6 \, \arctan \left (t^{\frac{1}{6}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(t)/(t^(1/3) + 1),t, algorithm="fricas")
[Out]
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Sympy [A] time = 4.80965, size = 37, normalized size = 0.9 \[ \frac{6 t^{\frac{7}{6}}}{7} - \frac{6 t^{\frac{5}{6}}}{5} - 6 \sqrt [6]{t} + 2 \sqrt{t} + 6 \operatorname{atan}{\left (\sqrt [6]{t} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t**(1/2)/(1+t**(1/3)),t)
[Out]
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GIAC/XCAS [A] time = 0.213486, size = 36, normalized size = 0.88 \[ \frac{6}{7} \, t^{\frac{7}{6}} - \frac{6}{5} \, t^{\frac{5}{6}} + 2 \, \sqrt{t} - 6 \, t^{\frac{1}{6}} + 6 \, \arctan \left (t^{\frac{1}{6}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(t)/(t^(1/3) + 1),t, algorithm="giac")
[Out]