3.1554 \(\int \frac{a+\frac{b}{x}}{x^4} \, dx\)

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

[Out]

-b/(4*x^4) - a/(3*x^3)

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Rubi [A]  time = 0.0154677, antiderivative size = 17, 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 \[ -\frac{a}{3 x^3}-\frac{b}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)/x^4,x]

[Out]

-b/(4*x^4) - a/(3*x^3)

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Rubi in Sympy [A]  time = 2.94198, size = 14, normalized size = 0.82 \[ - \frac{a}{3 x^{3}} - \frac{b}{4 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x)/x**4,x)

[Out]

-a/(3*x**3) - b/(4*x**4)

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Mathematica [A]  time = 0.00267858, size = 17, normalized size = 1. \[ -\frac{a}{3 x^3}-\frac{b}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)/x^4,x]

[Out]

-b/(4*x^4) - a/(3*x^3)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)/x^4,x)

[Out]

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

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Maxima [A]  time = 1.41674, size = 18, normalized size = 1.06 \[ -\frac{4 \, a x + 3 \, b}{12 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x)/x^4,x, algorithm="maxima")

[Out]

-1/12*(4*a*x + 3*b)/x^4

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Fricas [A]  time = 0.218068, size = 18, normalized size = 1.06 \[ -\frac{4 \, a x + 3 \, b}{12 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x)/x^4,x, algorithm="fricas")

[Out]

-1/12*(4*a*x + 3*b)/x^4

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Sympy [A]  time = 1.11283, size = 14, normalized size = 0.82 \[ - \frac{4 a x + 3 b}{12 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)/x**4,x)

[Out]

-(4*a*x + 3*b)/(12*x**4)

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GIAC/XCAS [A]  time = 0.224499, size = 18, normalized size = 1.06 \[ -\frac{4 \, a x + 3 \, b}{12 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x)/x^4,x, algorithm="giac")

[Out]

-1/12*(4*a*x + 3*b)/x^4