3.217 \(\int \frac{a+b x^3}{x^8} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{7 x^7}-\frac{b}{4 x^4} \]

[Out]

-a/(7*x^7) - b/(4*x^4)

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Rubi [A]  time = 0.0129049, 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 \[ -\frac{a}{7 x^7}-\frac{b}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)/x^8,x]

[Out]

-a/(7*x^7) - b/(4*x^4)

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Rubi in Sympy [A]  time = 3.03938, size = 14, normalized size = 0.82 \[ - \frac{a}{7 x^{7}} - \frac{b}{4 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)/x**8,x)

[Out]

-a/(7*x**7) - b/(4*x**4)

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Mathematica [A]  time = 0.00395147, size = 17, normalized size = 1. \[ -\frac{a}{7 x^7}-\frac{b}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)/x^8,x]

[Out]

-a/(7*x^7) - b/(4*x^4)

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Maple [A]  time = 0.006, size = 14, normalized size = 0.8 \[ -{\frac{a}{7\,{x}^{7}}}-{\frac{b}{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)/x^8,x)

[Out]

-1/7*a/x^7-1/4*b/x^4

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Maxima [A]  time = 1.42145, size = 20, normalized size = 1.18 \[ -\frac{7 \, b x^{3} + 4 \, a}{28 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^8,x, algorithm="maxima")

[Out]

-1/28*(7*b*x^3 + 4*a)/x^7

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Fricas [A]  time = 0.210809, size = 20, normalized size = 1.18 \[ -\frac{7 \, b x^{3} + 4 \, a}{28 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^8,x, algorithm="fricas")

[Out]

-1/28*(7*b*x^3 + 4*a)/x^7

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Sympy [A]  time = 1.21268, size = 15, normalized size = 0.88 \[ - \frac{4 a + 7 b x^{3}}{28 x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)/x**8,x)

[Out]

-(4*a + 7*b*x**3)/(28*x**7)

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GIAC/XCAS [A]  time = 0.215813, size = 20, normalized size = 1.18 \[ -\frac{7 \, b x^{3} + 4 \, a}{28 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^8,x, algorithm="giac")

[Out]

-1/28*(7*b*x^3 + 4*a)/x^7