3.615 \(\int \frac{a+b x^4}{x^8} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{7 x^7}-\frac{b}{3 x^3} \]

[Out]

-a/(7*x^7) - b/(3*x^3)

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Rubi [A]  time = 0.0136524, 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 \[ -\frac{a}{7 x^7}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^4)/x^8,x]

[Out]

-a/(7*x^7) - b/(3*x^3)

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Rubi in Sympy [A]  time = 2.94884, size = 14, normalized size = 0.82 \[ - \frac{a}{7 x^{7}} - \frac{b}{3 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**4+a)/x**8,x)

[Out]

-a/(7*x**7) - b/(3*x**3)

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Mathematica [A]  time = 0.00350285, size = 17, normalized size = 1. \[ -\frac{a}{7 x^7}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^4)/x^8,x]

[Out]

-a/(7*x^7) - b/(3*x^3)

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Maple [A]  time = 0.007, size = 14, normalized size = 0.8 \[ -{\frac{a}{7\,{x}^{7}}}-{\frac{b}{3\,{x}^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^4+a)/x^8,x)

[Out]

-1/7*a/x^7-1/3*b/x^3

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Maxima [A]  time = 1.44075, size = 20, normalized size = 1.18 \[ -\frac{7 \, b x^{4} + 3 \, a}{21 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^8,x, algorithm="maxima")

[Out]

-1/21*(7*b*x^4 + 3*a)/x^7

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Fricas [A]  time = 0.217145, size = 20, normalized size = 1.18 \[ -\frac{7 \, b x^{4} + 3 \, a}{21 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^8,x, algorithm="fricas")

[Out]

-1/21*(7*b*x^4 + 3*a)/x^7

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Sympy [A]  time = 1.16746, size = 15, normalized size = 0.88 \[ - \frac{3 a + 7 b x^{4}}{21 x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**4+a)/x**8,x)

[Out]

-(3*a + 7*b*x**4)/(21*x**7)

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GIAC/XCAS [A]  time = 0.233702, size = 20, normalized size = 1.18 \[ -\frac{7 \, b x^{4} + 3 \, a}{21 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^8,x, algorithm="giac")

[Out]

-1/21*(7*b*x^4 + 3*a)/x^7