3.2439 \(\int x^{2/3} \left (1+x^{5/3}\right )^{2/3} \, dx\)

Optimal. Leaf size=15 \[ \frac{9}{25} \left (x^{5/3}+1\right )^{5/3} \]

[Out]

(9*(1 + x^(5/3))^(5/3))/25

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Rubi [A]  time = 0.0140645, 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 \[ \frac{9}{25} \left (x^{5/3}+1\right )^{5/3} \]

Antiderivative was successfully verified.

[In]  Int[x^(2/3)*(1 + x^(5/3))^(2/3),x]

[Out]

(9*(1 + x^(5/3))^(5/3))/25

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Rubi in Sympy [A]  time = 1.66251, size = 12, normalized size = 0.8 \[ \frac{9 \left (x^{\frac{5}{3}} + 1\right )^{\frac{5}{3}}}{25} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**(2/3)*(1+x**(5/3))**(2/3),x)

[Out]

9*(x**(5/3) + 1)**(5/3)/25

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Mathematica [A]  time = 0.00807221, size = 15, normalized size = 1. \[ \frac{9}{25} \left (x^{5/3}+1\right )^{5/3} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(2/3)*(1 + x^(5/3))^(2/3),x]

[Out]

(9*(1 + x^(5/3))^(5/3))/25

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Maple [A]  time = 0.003, size = 10, normalized size = 0.7 \[{\frac{9}{25} \left ( 1+{x}^{{\frac{5}{3}}} \right ) ^{{\frac{5}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^(2/3)*(1+x^(5/3))^(2/3),x)

[Out]

9/25*(1+x^(5/3))^(5/3)

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Maxima [A]  time = 1.43765, size = 12, normalized size = 0.8 \[ \frac{9}{25} \,{\left (x^{\frac{5}{3}} + 1\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^(5/3) + 1)^(2/3)*x^(2/3),x, algorithm="maxima")

[Out]

9/25*(x^(5/3) + 1)^(5/3)

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Fricas [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^(5/3) + 1)^(2/3)*x^(2/3),x, algorithm="fricas")

[Out]

Timed out

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Sympy [A]  time = 6.24355, size = 31, normalized size = 2.07 \[ \frac{9 x^{\frac{5}{3}} \left (x^{\frac{5}{3}} + 1\right )^{\frac{2}{3}}}{25} + \frac{9 \left (x^{\frac{5}{3}} + 1\right )^{\frac{2}{3}}}{25} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**(2/3)*(1+x**(5/3))**(2/3),x)

[Out]

9*x**(5/3)*(x**(5/3) + 1)**(2/3)/25 + 9*(x**(5/3) + 1)**(2/3)/25

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int{\left (x^{\frac{5}{3}} + 1\right )}^{\frac{2}{3}} x^{\frac{2}{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^(5/3) + 1)^(2/3)*x^(2/3),x, algorithm="giac")

[Out]

integrate((x^(5/3) + 1)^(2/3)*x^(2/3), x)