3.23 \(\int \frac{1}{d x^3} \, dx\)

Optimal. Leaf size=10 \[ -\frac{1}{2 d x^2} \]

[Out]

-1/(2*d*x^2)

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Rubi [A]  time = 0.00546883, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ -\frac{1}{2 d x^2} \]

Antiderivative was successfully verified.

[In]  Int[1/(d*x^3),x]

[Out]

-1/(2*d*x^2)

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Rubi in Sympy [A]  time = 1.54964, size = 8, normalized size = 0.8 \[ - \frac{1}{2 d x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/d/x**3,x)

[Out]

-1/(2*d*x**2)

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Mathematica [A]  time = 0.00056349, size = 10, normalized size = 1. \[ -\frac{1}{2 d x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[1/(d*x^3),x]

[Out]

-1/(2*d*x^2)

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Maple [A]  time = 0.001, size = 9, normalized size = 0.9 \[ -{\frac{1}{2\,d{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/d/x^3,x)

[Out]

-1/2/d/x^2

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Maxima [A]  time = 0.769606, size = 11, normalized size = 1.1 \[ -\frac{1}{2 \, d x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2/(d*x^2)

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Fricas [A]  time = 0.298204, size = 11, normalized size = 1.1 \[ -\frac{1}{2 \, d x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2/(d*x^2)

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Sympy [A]  time = 0.071728, size = 8, normalized size = 0.8 \[ - \frac{1}{2 d x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/d/x**3,x)

[Out]

-1/(2*d*x**2)

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GIAC/XCAS [A]  time = 0.260774, size = 11, normalized size = 1.1 \[ -\frac{1}{2 \, d x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2/(d*x^2)