3.1407 \(\int \frac{x^{17}}{\left (2+x^6\right )^{3/2}} \, dx\)

Optimal. Leaf size=40 \[ \frac{1}{9} \left (x^6+2\right )^{3/2}-\frac{4 \sqrt{x^6+2}}{3}-\frac{4}{3 \sqrt{x^6+2}} \]

[Out]

-4/(3*Sqrt[2 + x^6]) - (4*Sqrt[2 + x^6])/3 + (2 + x^6)^(3/2)/9

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Rubi [A]  time = 0.0402759, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{9} \left (x^6+2\right )^{3/2}-\frac{4 \sqrt{x^6+2}}{3}-\frac{4}{3 \sqrt{x^6+2}} \]

Antiderivative was successfully verified.

[In]  Int[x^17/(2 + x^6)^(3/2),x]

[Out]

-4/(3*Sqrt[2 + x^6]) - (4*Sqrt[2 + x^6])/3 + (2 + x^6)^(3/2)/9

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Rubi in Sympy [A]  time = 4.51056, size = 32, normalized size = 0.8 \[ \frac{\left (x^{6} + 2\right )^{\frac{3}{2}}}{9} - \frac{4 \sqrt{x^{6} + 2}}{3} - \frac{4}{3 \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**17/(x**6+2)**(3/2),x)

[Out]

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

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Mathematica [A]  time = 0.0150235, size = 23, normalized size = 0.57 \[ \frac{x^{12}-8 x^6-32}{9 \sqrt{x^6+2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^17/(2 + x^6)^(3/2),x]

[Out]

(-32 - 8*x^6 + x^12)/(9*Sqrt[2 + x^6])

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Maple [A]  time = 0.008, size = 20, normalized size = 0.5 \[{\frac{{x}^{12}-8\,{x}^{6}-32}{9}{\frac{1}{\sqrt{{x}^{6}+2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^17/(x^6+2)^(3/2),x)

[Out]

1/9*(x^12-8*x^6-32)/(x^6+2)^(1/2)

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Maxima [A]  time = 1.43212, size = 38, normalized size = 0.95 \[ \frac{1}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} - \frac{4}{3} \, \sqrt{x^{6} + 2} - \frac{4}{3 \, \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^17/(x^6 + 2)^(3/2),x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0.215712, size = 26, normalized size = 0.65 \[ \frac{x^{12} - 8 \, x^{6} - 32}{9 \, \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^17/(x^6 + 2)^(3/2),x, algorithm="fricas")

[Out]

1/9*(x^12 - 8*x^6 - 32)/sqrt(x^6 + 2)

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Sympy [A]  time = 19.2386, size = 39, normalized size = 0.98 \[ \frac{x^{12}}{9 \sqrt{x^{6} + 2}} - \frac{8 x^{6}}{9 \sqrt{x^{6} + 2}} - \frac{32}{9 \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**17/(x**6+2)**(3/2),x)

[Out]

x**12/(9*sqrt(x**6 + 2)) - 8*x**6/(9*sqrt(x**6 + 2)) - 32/(9*sqrt(x**6 + 2))

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GIAC/XCAS [A]  time = 0.2219, size = 38, normalized size = 0.95 \[ \frac{1}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} - \frac{4}{3} \, \sqrt{x^{6} + 2} - \frac{4}{3 \, \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^17/(x^6 + 2)^(3/2),x, algorithm="giac")

[Out]

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