3.487 \(\int \frac{-1+x^3}{-1+x} \, dx\)

Optimal. Leaf size=16 \[ \frac{x^3}{3}+\frac{x^2}{2}+x \]

[Out]

x + x^2/2 + x^3/3

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Rubi [A]  time = 0.0118253, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x^3}{3}+\frac{x^2}{2}+x \]

Antiderivative was successfully verified.

[In]  Int[(-1 + x^3)/(-1 + x),x]

[Out]

x + x^2/2 + x^3/3

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**3/3 + x + Integral(x, x)

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Mathematica [A]  time = 0.000656925, size = 16, normalized size = 1. \[ \frac{x^3}{3}+\frac{x^2}{2}+x \]

Antiderivative was successfully verified.

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

[Out]

x + x^2/2 + x^3/3

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Maple [A]  time = 0.001, size = 13, normalized size = 0.8 \[ x+{\frac{{x}^{2}}{2}}+{\frac{{x}^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^3-1)/(-1+x),x)

[Out]

x+1/2*x^2+1/3*x^3

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Maxima [A]  time = 0.785423, size = 16, normalized size = 1. \[ \frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*x^3 + 1/2*x^2 + x

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Fricas [A]  time = 0.24503, size = 16, normalized size = 1. \[ \frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*x^3 + 1/2*x^2 + x

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Sympy [A]  time = 0.07334, size = 10, normalized size = 0.62 \[ \frac{x^{3}}{3} + \frac{x^{2}}{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**3-1)/(-1+x),x)

[Out]

x**3/3 + x**2/2 + x

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GIAC/XCAS [A]  time = 0.259049, size = 16, normalized size = 1. \[ \frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*x^3 + 1/2*x^2 + x