3.984 \(\int \frac{x^3}{\left (1+x^4\right )^{4/3}} \, dx\)

Optimal. Leaf size=13 \[ -\frac{3}{4 \sqrt [3]{x^4+1}} \]

[Out]

-3/(4*(1 + x^4)^(1/3))

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Rubi [A]  time = 0.00689211, 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 \[ -\frac{3}{4 \sqrt [3]{x^4+1}} \]

Antiderivative was successfully verified.

[In]  Int[x^3/(1 + x^4)^(4/3),x]

[Out]

-3/(4*(1 + x^4)^(1/3))

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Rubi in Sympy [A]  time = 1.6376, size = 12, normalized size = 0.92 \[ - \frac{3}{4 \sqrt [3]{x^{4} + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3/(x**4+1)**(4/3),x)

[Out]

-3/(4*(x**4 + 1)**(1/3))

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Mathematica [A]  time = 0.00550883, size = 13, normalized size = 1. \[ -\frac{3}{4 \sqrt [3]{x^4+1}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3/(1 + x^4)^(4/3),x]

[Out]

-3/(4*(1 + x^4)^(1/3))

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Maple [A]  time = 0.005, size = 10, normalized size = 0.8 \[ -{\frac{3}{4}{\frac{1}{\sqrt [3]{{x}^{4}+1}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3/(x^4+1)^(4/3),x)

[Out]

-3/4/(x^4+1)^(1/3)

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Maxima [A]  time = 1.41986, size = 12, normalized size = 0.92 \[ -\frac{3}{4 \,{\left (x^{4} + 1\right )}^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(x^4 + 1)^(4/3),x, algorithm="maxima")

[Out]

-3/4/(x^4 + 1)^(1/3)

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Fricas [A]  time = 0.251176, size = 12, normalized size = 0.92 \[ -\frac{3}{4 \,{\left (x^{4} + 1\right )}^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(x^4 + 1)^(4/3),x, algorithm="fricas")

[Out]

-3/4/(x^4 + 1)^(1/3)

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Sympy [A]  time = 1.54353, size = 12, normalized size = 0.92 \[ - \frac{3}{4 \sqrt [3]{x^{4} + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3/(x**4+1)**(4/3),x)

[Out]

-3/(4*(x**4 + 1)**(1/3))

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GIAC/XCAS [A]  time = 0.214483, size = 12, normalized size = 0.92 \[ -\frac{3}{4 \,{\left (x^{4} + 1\right )}^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(x^4 + 1)^(4/3),x, algorithm="giac")

[Out]

-3/4/(x^4 + 1)^(1/3)