3.58 \(\int \frac{\sqrt [3]{1-x^3}}{1+x} \, dx\)

Optimal. Leaf size=1 \[ 0 \]

[Out]

0

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Rubi [F]  time = 0.0989775, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{\sqrt [3]{1-x^3}}{1+x},x\right ) \]

Verification is Not applicable to the result.

[In]  Int[(1 - x^3)^(1/3)/(1 + x),x]

[Out]

Defer[Int][(1 - x^3)^(1/3)/(1 + x), x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt [3]{- x^{3} + 1}}{x + 1}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Integral((-x**3 + 1)**(1/3)/(x + 1), x)

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Mathematica [A]  time = 0.371783, size = 0, normalized size = 0. \[ \int \frac{\sqrt [3]{1-x^3}}{1+x} \, dx \]

Verification is Not applicable to the result.

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

[Out]

Integrate[(1 - x^3)^(1/3)/(1 + x), x]

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Maple [F]  time = 0.072, size = 0, normalized size = 0. \[ \int{\frac{1}{1+x}\sqrt [3]{-{x}^{3}+1}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-x^3+1)^(1/3)/(1+x),x)

[Out]

int((-x^3+1)^(1/3)/(1+x),x)

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (-x^{3} + 1\right )}^{\frac{1}{3}}}{x + 1}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate((-x^3 + 1)^(1/3)/(x + 1), x)

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Exception raised: TypeError

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt [3]{- \left (x - 1\right ) \left (x^{2} + x + 1\right )}}{x + 1}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Integral((-(x - 1)*(x**2 + x + 1))**(1/3)/(x + 1), x)

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (-x^{3} + 1\right )}^{\frac{1}{3}}}{x + 1}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate((-x^3 + 1)^(1/3)/(x + 1), x)