3.193 \(\int \frac{x}{\left (1-x^2\right )^{9/8}} \, dx\)

Optimal. Leaf size=13 \[ \frac{4}{\sqrt [8]{1-x^2}} \]

[Out]

4/(1 - x^2)^(1/8)

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Rubi [A]  time = 0.00582945, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{4}{\sqrt [8]{1-x^2}} \]

Antiderivative was successfully verified.

[In]  Int[x/(1 - x^2)^(9/8),x]

[Out]

4/(1 - x^2)^(1/8)

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Rubi in Sympy [A]  time = 0.911313, size = 8, normalized size = 0.62 \[ \frac{4}{\sqrt [8]{- x^{2} + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x/(-x**2+1)**(9/8),x)

[Out]

4/(-x**2 + 1)**(1/8)

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Mathematica [A]  time = 0.00365069, size = 13, normalized size = 1. \[ \frac{4}{\sqrt [8]{1-x^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x/(1 - x^2)^(9/8),x]

[Out]

4/(1 - x^2)^(1/8)

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Maple [A]  time = 0.002, size = 18, normalized size = 1.4 \[ -4\,{ \left ( -1+x \right ) \left ( 1+x \right ) \left ( -{x}^{2}+1 \right ) ^{-{\frac{9}{8}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(-x^2+1)^(9/8),x)

[Out]

-4*(-1+x)*(1+x)/(-x^2+1)^(9/8)

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Maxima [A]  time = 1.3864, size = 15, normalized size = 1.15 \[ \frac{4}{{\left (-x^{2} + 1\right )}^{\frac{1}{8}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(-x^2 + 1)^(9/8),x, algorithm="maxima")

[Out]

4/(-x^2 + 1)^(1/8)

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Fricas [A]  time = 0.211273, size = 15, normalized size = 1.15 \[ \frac{4}{{\left (-x^{2} + 1\right )}^{\frac{1}{8}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(-x^2 + 1)^(9/8),x, algorithm="fricas")

[Out]

4/(-x^2 + 1)^(1/8)

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Sympy [A]  time = 1.78034, size = 8, normalized size = 0.62 \[ \frac{4}{\sqrt [8]{- x^{2} + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(-x**2+1)**(9/8),x)

[Out]

4/(-x**2 + 1)**(1/8)

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GIAC/XCAS [A]  time = 0.201328, size = 15, normalized size = 1.15 \[ \frac{4}{{\left (-x^{2} + 1\right )}^{\frac{1}{8}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(-x^2 + 1)^(9/8),x, algorithm="giac")

[Out]

4/(-x^2 + 1)^(1/8)