3.216 \(\int \frac{a+b x^3}{x^7} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{6 x^6}-\frac{b}{3 x^3} \]

[Out]

-a/(6*x^6) - b/(3*x^3)

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Rubi [A]  time = 0.0133107, 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 \[ -\frac{a}{6 x^6}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)/x^7,x]

[Out]

-a/(6*x^6) - b/(3*x^3)

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Rubi in Sympy [A]  time = 2.97224, size = 14, normalized size = 0.82 \[ - \frac{a}{6 x^{6}} - \frac{b}{3 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)/x**7,x)

[Out]

-a/(6*x**6) - b/(3*x**3)

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Mathematica [A]  time = 0.00375596, size = 17, normalized size = 1. \[ -\frac{a}{6 x^6}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)/x^7,x]

[Out]

-a/(6*x^6) - b/(3*x^3)

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Maple [A]  time = 0.006, size = 14, normalized size = 0.8 \[ -{\frac{a}{6\,{x}^{6}}}-{\frac{b}{3\,{x}^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)/x^7,x)

[Out]

-1/6*a/x^6-1/3*b/x^3

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Maxima [A]  time = 1.43564, size = 18, normalized size = 1.06 \[ -\frac{2 \, b x^{3} + a}{6 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^7,x, algorithm="maxima")

[Out]

-1/6*(2*b*x^3 + a)/x^6

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Fricas [A]  time = 0.207749, size = 18, normalized size = 1.06 \[ -\frac{2 \, b x^{3} + a}{6 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^7,x, algorithm="fricas")

[Out]

-1/6*(2*b*x^3 + a)/x^6

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Sympy [A]  time = 1.19903, size = 14, normalized size = 0.82 \[ - \frac{a + 2 b x^{3}}{6 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)/x**7,x)

[Out]

-(a + 2*b*x**3)/(6*x**6)

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GIAC/XCAS [A]  time = 0.215202, size = 18, normalized size = 1.06 \[ -\frac{2 \, b x^{3} + a}{6 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^7,x, algorithm="giac")

[Out]

-1/6*(2*b*x^3 + a)/x^6