3.62 \(\int \frac{(a+b x)^2}{x^7} \, dx\)

Optimal. Leaf size=30 \[ -\frac{a^2}{6 x^6}-\frac{2 a b}{5 x^5}-\frac{b^2}{4 x^4} \]

[Out]

-a^2/(6*x^6) - (2*a*b)/(5*x^5) - b^2/(4*x^4)

_______________________________________________________________________________________

Rubi [A]  time = 0.0229745, 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 \[ -\frac{a^2}{6 x^6}-\frac{2 a b}{5 x^5}-\frac{b^2}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^2/x^7,x]

[Out]

-a^2/(6*x^6) - (2*a*b)/(5*x^5) - b^2/(4*x^4)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 4.47366, size = 27, normalized size = 0.9 \[ - \frac{a^{2}}{6 x^{6}} - \frac{2 a b}{5 x^{5}} - \frac{b^{2}}{4 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**2/x**7,x)

[Out]

-a**2/(6*x**6) - 2*a*b/(5*x**5) - b**2/(4*x**4)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00445448, size = 30, normalized size = 1. \[ -\frac{a^2}{6 x^6}-\frac{2 a b}{5 x^5}-\frac{b^2}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^2/x^7,x]

[Out]

-a^2/(6*x^6) - (2*a*b)/(5*x^5) - b^2/(4*x^4)

_______________________________________________________________________________________

Maple [A]  time = 0.007, size = 25, normalized size = 0.8 \[ -{\frac{{a}^{2}}{6\,{x}^{6}}}-{\frac{2\,ab}{5\,{x}^{5}}}-{\frac{{b}^{2}}{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^2/x^7,x)

[Out]

-1/6*a^2/x^6-2/5*a*b/x^5-1/4*b^2/x^4

_______________________________________________________________________________________

Maxima [A]  time = 1.33554, size = 32, normalized size = 1.07 \[ -\frac{15 \, b^{2} x^{2} + 24 \, a b x + 10 \, a^{2}}{60 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^2/x^7,x, algorithm="maxima")

[Out]

-1/60*(15*b^2*x^2 + 24*a*b*x + 10*a^2)/x^6

_______________________________________________________________________________________

Fricas [A]  time = 0.210476, size = 32, normalized size = 1.07 \[ -\frac{15 \, b^{2} x^{2} + 24 \, a b x + 10 \, a^{2}}{60 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^2/x^7,x, algorithm="fricas")

[Out]

-1/60*(15*b^2*x^2 + 24*a*b*x + 10*a^2)/x^6

_______________________________________________________________________________________

Sympy [A]  time = 1.31469, size = 26, normalized size = 0.87 \[ - \frac{10 a^{2} + 24 a b x + 15 b^{2} x^{2}}{60 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**2/x**7,x)

[Out]

-(10*a**2 + 24*a*b*x + 15*b**2*x**2)/(60*x**6)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.209409, size = 32, normalized size = 1.07 \[ -\frac{15 \, b^{2} x^{2} + 24 \, a b x + 10 \, a^{2}}{60 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^2/x^7,x, algorithm="giac")

[Out]

-1/60*(15*b^2*x^2 + 24*a*b*x + 10*a^2)/x^6