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

Optimal. Leaf size=17 \[ -\frac{a}{3 x^3}-\frac{b}{2 x^2} \]

[Out]

-a/(3*x^3) - b/(2*x^2)

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Rubi [A]  time = 0.0145026, 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 \[ -\frac{a}{3 x^3}-\frac{b}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)/x^4,x]

[Out]

-a/(3*x^3) - b/(2*x^2)

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Rubi in Sympy [A]  time = 2.53299, size = 14, normalized size = 0.82 \[ - \frac{a}{3 x^{3}} - \frac{b}{2 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)/x**4,x)

[Out]

-a/(3*x**3) - b/(2*x**2)

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Mathematica [A]  time = 0.00279633, size = 17, normalized size = 1. \[ -\frac{a}{3 x^3}-\frac{b}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)/x^4,x]

[Out]

-a/(3*x^3) - b/(2*x^2)

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Maple [A]  time = 0.007, size = 14, normalized size = 0.8 \[ -{\frac{a}{3\,{x}^{3}}}-{\frac{b}{2\,{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)/x^4,x)

[Out]

-1/3*a/x^3-1/2*b/x^2

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Maxima [A]  time = 1.44602, size = 18, normalized size = 1.06 \[ -\frac{3 \, b x + 2 \, a}{6 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6*(3*b*x + 2*a)/x^3

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Fricas [A]  time = 0.188437, size = 18, normalized size = 1.06 \[ -\frac{3 \, b x + 2 \, a}{6 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6*(3*b*x + 2*a)/x^3

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Sympy [A]  time = 1.07389, size = 14, normalized size = 0.82 \[ - \frac{2 a + 3 b x}{6 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)/x**4,x)

[Out]

-(2*a + 3*b*x)/(6*x**3)

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GIAC/XCAS [A]  time = 0.207929, size = 18, normalized size = 1.06 \[ -\frac{3 \, b x + 2 \, a}{6 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6*(3*b*x + 2*a)/x^3