3.2440 \(\int x^{7/3} \left (a^{10/3}-x^{10/3}\right )^{19/7} \, dx\)

Optimal. Leaf size=21 \[ -\frac{21}{260} \left (a^{10/3}-x^{10/3}\right )^{26/7} \]

[Out]

(-21*(a^(10/3) - x^(10/3))^(26/7))/260

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Rubi [A]  time = 0.0188208, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043 \[ -\frac{21}{260} \left (a^{10/3}-x^{10/3}\right )^{26/7} \]

Antiderivative was successfully verified.

[In]  Int[x^(7/3)*(a^(10/3) - x^(10/3))^(19/7),x]

[Out]

(-21*(a^(10/3) - x^(10/3))^(26/7))/260

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Rubi in Sympy [A]  time = 2.10471, size = 17, normalized size = 0.81 \[ - \frac{21 \left (a^{\frac{10}{3}} - x^{\frac{10}{3}}\right )^{\frac{26}{7}}}{260} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**(7/3)*(a**(10/3)-x**(10/3))**(19/7),x)

[Out]

-21*(a**(10/3) - x**(10/3))**(26/7)/260

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Mathematica [A]  time = 0.0194828, size = 21, normalized size = 1. \[ -\frac{21}{260} \left (a^{10/3}-x^{10/3}\right )^{26/7} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(7/3)*(a^(10/3) - x^(10/3))^(19/7),x]

[Out]

(-21*(a^(10/3) - x^(10/3))^(26/7))/260

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Maple [A]  time = 0.003, size = 14, normalized size = 0.7 \[ -{\frac{21}{260} \left ({a}^{{\frac{10}{3}}}-{x}^{{\frac{10}{3}}} \right ) ^{{\frac{26}{7}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^(7/3)*(a^(10/3)-x^(10/3))^(19/7),x)

[Out]

-21/260*(a^(10/3)-x^(10/3))^(26/7)

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Maxima [A]  time = 1.43771, size = 18, normalized size = 0.86 \[ -\frac{21}{260} \,{\left (a^{\frac{10}{3}} - x^{\frac{10}{3}}\right )}^{\frac{26}{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a^(10/3) - x^(10/3))^(19/7)*x^(7/3),x, algorithm="maxima")

[Out]

-21/260*(a^(10/3) - x^(10/3))^(26/7)

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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((a^(10/3) - x^(10/3))^(19/7)*x^(7/3),x, algorithm="fricas")

[Out]

Timed out

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Sympy [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**(7/3)*(a**(10/3)-x**(10/3))**(19/7),x)

[Out]

Timed out

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int{\left (a^{\frac{10}{3}} - x^{\frac{10}{3}}\right )}^{\frac{19}{7}} x^{\frac{7}{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a^(10/3) - x^(10/3))^(19/7)*x^(7/3),x, algorithm="giac")

[Out]

integrate((a^(10/3) - x^(10/3))^(19/7)*x^(7/3), x)