3.63 \(\int \frac{(a+b x)^2}{x^8} \, dx\)

Optimal. Leaf size=30 \[ -\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5} \]

[Out]

-a^2/(7*x^7) - (a*b)/(3*x^6) - b^2/(5*x^5)

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Rubi [A]  time = 0.0237536, antiderivative size = 30, 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 \[ -\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^2/x^8,x]

[Out]

-a^2/(7*x^7) - (a*b)/(3*x^6) - b^2/(5*x^5)

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Rubi in Sympy [A]  time = 4.552, size = 26, normalized size = 0.87 \[ - \frac{a^{2}}{7 x^{7}} - \frac{a b}{3 x^{6}} - \frac{b^{2}}{5 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**2/x**8,x)

[Out]

-a**2/(7*x**7) - a*b/(3*x**6) - b**2/(5*x**5)

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Mathematica [A]  time = 0.00900848, size = 30, normalized size = 1. \[ -\frac{a^2}{7 x^7}-\frac{a b}{3 x^6}-\frac{b^2}{5 x^5} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^2/x^8,x]

[Out]

-a^2/(7*x^7) - (a*b)/(3*x^6) - b^2/(5*x^5)

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Maple [A]  time = 0.007, size = 25, normalized size = 0.8 \[ -{\frac{{a}^{2}}{7\,{x}^{7}}}-{\frac{ab}{3\,{x}^{6}}}-{\frac{{b}^{2}}{5\,{x}^{5}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^2/x^8,x)

[Out]

-1/7*a^2/x^7-1/3*a*b/x^6-1/5*b^2/x^5

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Maxima [A]  time = 1.32932, size = 32, normalized size = 1.07 \[ -\frac{21 \, b^{2} x^{2} + 35 \, a b x + 15 \, a^{2}}{105 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^2/x^8,x, algorithm="maxima")

[Out]

-1/105*(21*b^2*x^2 + 35*a*b*x + 15*a^2)/x^7

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Fricas [A]  time = 0.201019, size = 32, normalized size = 1.07 \[ -\frac{21 \, b^{2} x^{2} + 35 \, a b x + 15 \, a^{2}}{105 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^2/x^8,x, algorithm="fricas")

[Out]

-1/105*(21*b^2*x^2 + 35*a*b*x + 15*a^2)/x^7

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Sympy [A]  time = 1.35977, size = 26, normalized size = 0.87 \[ - \frac{15 a^{2} + 35 a b x + 21 b^{2} x^{2}}{105 x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**2/x**8,x)

[Out]

-(15*a**2 + 35*a*b*x + 21*b**2*x**2)/(105*x**7)

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GIAC/XCAS [A]  time = 0.209978, size = 32, normalized size = 1.07 \[ -\frac{21 \, b^{2} x^{2} + 35 \, a b x + 15 \, a^{2}}{105 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^2/x^8,x, algorithm="giac")

[Out]

-1/105*(21*b^2*x^2 + 35*a*b*x + 15*a^2)/x^7