3.250 \(\int \frac{a+b x}{x^{10}} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{9 x^9}-\frac{b}{8 x^8} \]

[Out]

-a/(9*x^9) - b/(8*x^8)

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Rubi [A]  time = 0.0144879, 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 \[ -\frac{a}{9 x^9}-\frac{b}{8 x^8} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)/x^10,x]

[Out]

-a/(9*x^9) - b/(8*x^8)

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Rubi in Sympy [A]  time = 2.67068, size = 14, normalized size = 0.82 \[ - \frac{a}{9 x^{9}} - \frac{b}{8 x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)/x**10,x)

[Out]

-a/(9*x**9) - b/(8*x**8)

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Mathematica [A]  time = 0.0027269, size = 17, normalized size = 1. \[ -\frac{a}{9 x^9}-\frac{b}{8 x^8} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)/x^10,x]

[Out]

-a/(9*x^9) - b/(8*x^8)

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Maple [A]  time = 0.009, size = 14, normalized size = 0.8 \[ -{\frac{a}{9\,{x}^{9}}}-{\frac{b}{8\,{x}^{8}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)/x^10,x)

[Out]

-1/9*a/x^9-1/8*b/x^8

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Maxima [A]  time = 1.34232, size = 18, normalized size = 1.06 \[ -\frac{9 \, b x + 8 \, a}{72 \, x^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)/x^10,x, algorithm="maxima")

[Out]

-1/72*(9*b*x + 8*a)/x^9

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Fricas [A]  time = 0.200919, size = 18, normalized size = 1.06 \[ -\frac{9 \, b x + 8 \, a}{72 \, x^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)/x^10,x, algorithm="fricas")

[Out]

-1/72*(9*b*x + 8*a)/x^9

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Sympy [A]  time = 1.24789, size = 14, normalized size = 0.82 \[ - \frac{8 a + 9 b x}{72 x^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)/x**10,x)

[Out]

-(8*a + 9*b*x)/(72*x**9)

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GIAC/XCAS [A]  time = 0.200296, size = 18, normalized size = 1.06 \[ -\frac{9 \, b x + 8 \, a}{72 \, x^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)/x^10,x, algorithm="giac")

[Out]

-1/72*(9*b*x + 8*a)/x^9