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

Optimal. Leaf size=17 \[ -\frac{a}{4 x^4}-\frac{b}{3 x^3} \]

[Out]

-a/(4*x^4) - b/(3*x^3)

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Rubi [A]  time = 0.0146728, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{a}{4 x^4}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)/x^5,x]

[Out]

-a/(4*x^4) - b/(3*x^3)

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Rubi in Sympy [A]  time = 2.60524, size = 14, normalized size = 0.82 \[ - \frac{a}{4 x^{4}} - \frac{b}{3 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)/x**5,x)

[Out]

-a/(4*x**4) - b/(3*x**3)

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Mathematica [A]  time = 0.00201429, size = 17, normalized size = 1. \[ -\frac{a}{4 x^4}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)/x^5,x]

[Out]

-a/(4*x^4) - b/(3*x^3)

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Maple [A]  time = 0.007, size = 14, normalized size = 0.8 \[ -{\frac{a}{4\,{x}^{4}}}-{\frac{b}{3\,{x}^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)/x^5,x)

[Out]

-1/4*a/x^4-1/3*b/x^3

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Maxima [A]  time = 1.32876, size = 18, normalized size = 1.06 \[ -\frac{4 \, b x + 3 \, a}{12 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/12*(4*b*x + 3*a)/x^4

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Fricas [A]  time = 0.196124, size = 18, normalized size = 1.06 \[ -\frac{4 \, b x + 3 \, a}{12 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/12*(4*b*x + 3*a)/x^4

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Sympy [A]  time = 1.10327, size = 14, normalized size = 0.82 \[ - \frac{3 a + 4 b x}{12 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)/x**5,x)

[Out]

-(3*a + 4*b*x)/(12*x**4)

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GIAC/XCAS [A]  time = 0.209652, size = 18, normalized size = 1.06 \[ -\frac{4 \, b x + 3 \, a}{12 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/12*(4*b*x + 3*a)/x^4