Optimal. Leaf size=15 \[ \frac{3}{5} \left (x^{2/3}+1\right )^{5/2} \]
[Out]
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Rubi [A] time = 0.0135666, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{3}{5} \left (x^{2/3}+1\right )^{5/2} \]
Antiderivative was successfully verified.
[In] Int[(1 + x^(2/3))^(3/2)/x^(1/3),x]
[Out]
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Rubi in Sympy [A] time = 1.66932, size = 12, normalized size = 0.8 \[ \frac{3 \left (x^{\frac{2}{3}} + 1\right )^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x**(2/3))**(3/2)/x**(1/3),x)
[Out]
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Mathematica [A] time = 0.00905232, size = 15, normalized size = 1. \[ \frac{3}{5} \left (x^{2/3}+1\right )^{5/2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^(2/3))^(3/2)/x^(1/3),x]
[Out]
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Maple [A] time = 0.008, size = 10, normalized size = 0.7 \[{\frac{3}{5} \left ( 1+{x}^{{\frac{2}{3}}} \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x^(2/3))^(3/2)/x^(1/3),x)
[Out]
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Maxima [A] time = 1.43581, size = 12, normalized size = 0.8 \[ \frac{3}{5} \,{\left (x^{\frac{2}{3}} + 1\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^(2/3) + 1)^(3/2)/x^(1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.935298, size = 26, normalized size = 1.73 \[ \frac{3}{5} \,{\left (x^{\frac{4}{3}} + 2 \, x^{\frac{2}{3}} + 1\right )} \sqrt{x^{\frac{2}{3}} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^(2/3) + 1)^(3/2)/x^(1/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.94053, size = 49, normalized size = 3.27 \[ \frac{3 x^{\frac{4}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{5} + \frac{6 x^{\frac{2}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{5} + \frac{3 \sqrt{x^{\frac{2}{3}} + 1}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x**(2/3))**(3/2)/x**(1/3),x)
[Out]
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GIAC/XCAS [A] time = 0.221197, size = 12, normalized size = 0.8 \[ \frac{3}{5} \,{\left (x^{\frac{2}{3}} + 1\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^(2/3) + 1)^(3/2)/x^(1/3),x, algorithm="giac")
[Out]