3.247 \(\int \frac{\left (a+b x^3\right )^3}{x^{19}} \, dx\)

Optimal. Leaf size=43 \[ -\frac{a^3}{18 x^{18}}-\frac{a^2 b}{5 x^{15}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9} \]

[Out]

-a^3/(18*x^18) - (a^2*b)/(5*x^15) - (a*b^2)/(4*x^12) - b^3/(9*x^9)

_______________________________________________________________________________________

Rubi [A]  time = 0.0530241, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^3}{18 x^{18}}-\frac{a^2 b}{5 x^{15}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^3/x^19,x]

[Out]

-a^3/(18*x^18) - (a^2*b)/(5*x^15) - (a*b^2)/(4*x^12) - b^3/(9*x^9)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 8.88161, size = 37, normalized size = 0.86 \[ - \frac{a^{3}}{18 x^{18}} - \frac{a^{2} b}{5 x^{15}} - \frac{a b^{2}}{4 x^{12}} - \frac{b^{3}}{9 x^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**3/x**19,x)

[Out]

-a**3/(18*x**18) - a**2*b/(5*x**15) - a*b**2/(4*x**12) - b**3/(9*x**9)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00680988, size = 43, normalized size = 1. \[ -\frac{a^3}{18 x^{18}}-\frac{a^2 b}{5 x^{15}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^3/x^19,x]

[Out]

-a^3/(18*x^18) - (a^2*b)/(5*x^15) - (a*b^2)/(4*x^12) - b^3/(9*x^9)

_______________________________________________________________________________________

Maple [A]  time = 0.009, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{18\,{x}^{18}}}-{\frac{{a}^{2}b}{5\,{x}^{15}}}-{\frac{a{b}^{2}}{4\,{x}^{12}}}-{\frac{{b}^{3}}{9\,{x}^{9}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^3/x^19,x)

[Out]

-1/18*a^3/x^18-1/5*a^2*b/x^15-1/4*a*b^2/x^12-1/9*b^3/x^9

_______________________________________________________________________________________

Maxima [A]  time = 1.44141, size = 50, normalized size = 1.16 \[ -\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^3/x^19,x, algorithm="maxima")

[Out]

-1/180*(20*b^3*x^9 + 45*a*b^2*x^6 + 36*a^2*b*x^3 + 10*a^3)/x^18

_______________________________________________________________________________________

Fricas [A]  time = 0.204639, size = 50, normalized size = 1.16 \[ -\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^3/x^19,x, algorithm="fricas")

[Out]

-1/180*(20*b^3*x^9 + 45*a*b^2*x^6 + 36*a^2*b*x^3 + 10*a^3)/x^18

_______________________________________________________________________________________

Sympy [A]  time = 2.11828, size = 39, normalized size = 0.91 \[ - \frac{10 a^{3} + 36 a^{2} b x^{3} + 45 a b^{2} x^{6} + 20 b^{3} x^{9}}{180 x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**3/x**19,x)

[Out]

-(10*a**3 + 36*a**2*b*x**3 + 45*a*b**2*x**6 + 20*b**3*x**9)/(180*x**18)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.221604, size = 50, normalized size = 1.16 \[ -\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^3/x^19,x, algorithm="giac")

[Out]

-1/180*(20*b^3*x^9 + 45*a*b^2*x^6 + 36*a^2*b*x^3 + 10*a^3)/x^18