3.214 \(\int \frac{a+b x^3}{x^5} \, dx\)

Optimal. Leaf size=15 \[ -\frac{a}{4 x^4}-\frac{b}{x} \]

[Out]

-a/(4*x^4) - b/x

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Rubi [A]  time = 0.0130067, antiderivative size = 15, 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 \[ -\frac{a}{4 x^4}-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)/x^5,x]

[Out]

-a/(4*x^4) - b/x

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Rubi in Sympy [A]  time = 2.93023, size = 10, normalized size = 0.67 \[ - \frac{a}{4 x^{4}} - \frac{b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)/x**5,x)

[Out]

-a/(4*x**4) - b/x

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Mathematica [A]  time = 0.00348301, size = 15, normalized size = 1. \[ -\frac{a}{4 x^4}-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)/x^5,x]

[Out]

-a/(4*x^4) - b/x

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Maple [A]  time = 0.006, size = 14, normalized size = 0.9 \[ -{\frac{a}{4\,{x}^{4}}}-{\frac{b}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)/x^5,x)

[Out]

-1/4*a/x^4-b/x

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Maxima [A]  time = 1.43768, size = 18, normalized size = 1.2 \[ -\frac{4 \, b x^{3} + a}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^5,x, algorithm="maxima")

[Out]

-1/4*(4*b*x^3 + a)/x^4

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Fricas [A]  time = 0.210331, size = 18, normalized size = 1.2 \[ -\frac{4 \, b x^{3} + a}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^5,x, algorithm="fricas")

[Out]

-1/4*(4*b*x^3 + a)/x^4

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Sympy [A]  time = 1.14706, size = 14, normalized size = 0.93 \[ - \frac{a + 4 b x^{3}}{4 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)/x**5,x)

[Out]

-(a + 4*b*x**3)/(4*x**4)

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GIAC/XCAS [A]  time = 0.213547, size = 18, normalized size = 1.2 \[ -\frac{4 \, b x^{3} + a}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^5,x, algorithm="giac")

[Out]

-1/4*(4*b*x^3 + a)/x^4