3.246 \(\int \frac{\left (a+b x^3\right )^3}{x^{16}} \, dx\)

Optimal. Leaf size=40 \[ \frac{b \left (a+b x^3\right )^4}{60 a^2 x^{12}}-\frac{\left (a+b x^3\right )^4}{15 a x^{15}} \]

[Out]

-(a + b*x^3)^4/(15*a*x^15) + (b*(a + b*x^3)^4)/(60*a^2*x^12)

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Rubi [A]  time = 0.0522817, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{b \left (a+b x^3\right )^4}{60 a^2 x^{12}}-\frac{\left (a+b x^3\right )^4}{15 a x^{15}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^3/x^16,x]

[Out]

-(a + b*x^3)^4/(15*a*x^15) + (b*(a + b*x^3)^4)/(60*a^2*x^12)

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Rubi in Sympy [A]  time = 8.75949, size = 37, normalized size = 0.92 \[ - \frac{a^{3}}{15 x^{15}} - \frac{a^{2} b}{4 x^{12}} - \frac{a b^{2}}{3 x^{9}} - \frac{b^{3}}{6 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**3/x**16,x)

[Out]

-a**3/(15*x**15) - a**2*b/(4*x**12) - a*b**2/(3*x**9) - b**3/(6*x**6)

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Mathematica [A]  time = 0.00671068, size = 43, normalized size = 1.08 \[ -\frac{a^3}{15 x^{15}}-\frac{a^2 b}{4 x^{12}}-\frac{a b^2}{3 x^9}-\frac{b^3}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^3/x^16,x]

[Out]

-a^3/(15*x^15) - (a^2*b)/(4*x^12) - (a*b^2)/(3*x^9) - b^3/(6*x^6)

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Maple [A]  time = 0.008, size = 36, normalized size = 0.9 \[ -{\frac{{a}^{2}b}{4\,{x}^{12}}}-{\frac{{a}^{3}}{15\,{x}^{15}}}-{\frac{{b}^{3}}{6\,{x}^{6}}}-{\frac{a{b}^{2}}{3\,{x}^{9}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^3/x^16,x)

[Out]

-1/4*a^2*b/x^12-1/15*a^3/x^15-1/6*b^3/x^6-1/3*a*b^2/x^9

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Maxima [A]  time = 1.4368, size = 50, normalized size = 1.25 \[ -\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^3/x^16,x, algorithm="maxima")

[Out]

-1/60*(10*b^3*x^9 + 20*a*b^2*x^6 + 15*a^2*b*x^3 + 4*a^3)/x^15

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Fricas [A]  time = 0.205513, size = 50, normalized size = 1.25 \[ -\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^3/x^16,x, algorithm="fricas")

[Out]

-1/60*(10*b^3*x^9 + 20*a*b^2*x^6 + 15*a^2*b*x^3 + 4*a^3)/x^15

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Sympy [A]  time = 1.96989, size = 39, normalized size = 0.98 \[ - \frac{4 a^{3} + 15 a^{2} b x^{3} + 20 a b^{2} x^{6} + 10 b^{3} x^{9}}{60 x^{15}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**3/x**16,x)

[Out]

-(4*a**3 + 15*a**2*b*x**3 + 20*a*b**2*x**6 + 10*b**3*x**9)/(60*x**15)

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GIAC/XCAS [A]  time = 0.214195, size = 50, normalized size = 1.25 \[ -\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^3/x^16,x, algorithm="giac")

[Out]

-1/60*(10*b^3*x^9 + 20*a*b^2*x^6 + 15*a^2*b*x^3 + 4*a^3)/x^15