3.701 \(\int x \left (-1+x^2\right )^{7/3} \, dx\)

Optimal. Leaf size=13 \[ \frac{3}{20} \left (x^2-1\right )^{10/3} \]

[Out]

(3*(-1 + x^2)^(10/3))/20

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Rubi [A]  time = 0.00776087, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{3}{20} \left (x^2-1\right )^{10/3} \]

Antiderivative was successfully verified.

[In]  Int[x*(-1 + x^2)^(7/3),x]

[Out]

(3*(-1 + x^2)^(10/3))/20

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Rubi in Sympy [A]  time = 1.63431, size = 10, normalized size = 0.77 \[ \frac{3 \left (x^{2} - 1\right )^{\frac{10}{3}}}{20} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x*(x**2-1)**(7/3),x)

[Out]

3*(x**2 - 1)**(10/3)/20

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Mathematica [A]  time = 0.00778583, size = 13, normalized size = 1. \[ \frac{3}{20} \left (x^2-1\right )^{10/3} \]

Antiderivative was successfully verified.

[In]  Integrate[x*(-1 + x^2)^(7/3),x]

[Out]

(3*(-1 + x^2)^(10/3))/20

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Maple [A]  time = 0.003, size = 16, normalized size = 1.2 \[{\frac{ \left ( -3+3\,x \right ) \left ( 1+x \right ) }{20} \left ({x}^{2}-1 \right ) ^{{\frac{7}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(x^2-1)^(7/3),x)

[Out]

3/20*(-1+x)*(1+x)*(x^2-1)^(7/3)

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Maxima [A]  time = 1.33677, size = 12, normalized size = 0.92 \[ \frac{3}{20} \,{\left (x^{2} - 1\right )}^{\frac{10}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 1)^(7/3)*x,x, algorithm="maxima")

[Out]

3/20*(x^2 - 1)^(10/3)

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Fricas [A]  time = 0.206275, size = 32, normalized size = 2.46 \[ \frac{3}{20} \,{\left (x^{6} - 3 \, x^{4} + 3 \, x^{2} - 1\right )}{\left (x^{2} - 1\right )}^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 1)^(7/3)*x,x, algorithm="fricas")

[Out]

3/20*(x^6 - 3*x^4 + 3*x^2 - 1)*(x^2 - 1)^(1/3)

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Sympy [A]  time = 10.4779, size = 56, normalized size = 4.31 \[ \frac{3 x^{6} \sqrt [3]{x^{2} - 1}}{20} - \frac{9 x^{4} \sqrt [3]{x^{2} - 1}}{20} + \frac{9 x^{2} \sqrt [3]{x^{2} - 1}}{20} - \frac{3 \sqrt [3]{x^{2} - 1}}{20} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(x**2-1)**(7/3),x)

[Out]

3*x**6*(x**2 - 1)**(1/3)/20 - 9*x**4*(x**2 - 1)**(1/3)/20 + 9*x**2*(x**2 - 1)**(
1/3)/20 - 3*(x**2 - 1)**(1/3)/20

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GIAC/XCAS [A]  time = 0.21132, size = 12, normalized size = 0.92 \[ \frac{3}{20} \,{\left (x^{2} - 1\right )}^{\frac{10}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 1)^(7/3)*x,x, algorithm="giac")

[Out]

3/20*(x^2 - 1)^(10/3)