3.248 \(\int \frac{\left (a+b x^3\right )^3}{x^{22}} \, dx\)

Optimal. Leaf size=43 \[ -\frac{a^3}{21 x^{21}}-\frac{a^2 b}{6 x^{18}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}} \]

[Out]

-a^3/(21*x^21) - (a^2*b)/(6*x^18) - (a*b^2)/(5*x^15) - b^3/(12*x^12)

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Rubi [A]  time = 0.0503132, 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 \[ -\frac{a^3}{21 x^{21}}-\frac{a^2 b}{6 x^{18}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^3/x^22,x]

[Out]

-a^3/(21*x^21) - (a^2*b)/(6*x^18) - (a*b^2)/(5*x^15) - b^3/(12*x^12)

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Rubi in Sympy [A]  time = 8.77914, size = 37, normalized size = 0.86 \[ - \frac{a^{3}}{21 x^{21}} - \frac{a^{2} b}{6 x^{18}} - \frac{a b^{2}}{5 x^{15}} - \frac{b^{3}}{12 x^{12}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**3/x**22,x)

[Out]

-a**3/(21*x**21) - a**2*b/(6*x**18) - a*b**2/(5*x**15) - b**3/(12*x**12)

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Mathematica [A]  time = 0.00678364, size = 43, normalized size = 1. \[ -\frac{a^3}{21 x^{21}}-\frac{a^2 b}{6 x^{18}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^3/x^22,x]

[Out]

-a^3/(21*x^21) - (a^2*b)/(6*x^18) - (a*b^2)/(5*x^15) - b^3/(12*x^12)

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Maple [A]  time = 0.009, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{21\,{x}^{21}}}-{\frac{{a}^{2}b}{6\,{x}^{18}}}-{\frac{a{b}^{2}}{5\,{x}^{15}}}-{\frac{{b}^{3}}{12\,{x}^{12}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^3/x^22,x)

[Out]

-1/21*a^3/x^21-1/6*a^2*b/x^18-1/5*a*b^2/x^15-1/12*b^3/x^12

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Maxima [A]  time = 1.46574, size = 50, normalized size = 1.16 \[ -\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^3/x^22,x, algorithm="maxima")

[Out]

-1/420*(35*b^3*x^9 + 84*a*b^2*x^6 + 70*a^2*b*x^3 + 20*a^3)/x^21

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Fricas [A]  time = 0.203003, size = 50, normalized size = 1.16 \[ -\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^3/x^22,x, algorithm="fricas")

[Out]

-1/420*(35*b^3*x^9 + 84*a*b^2*x^6 + 70*a^2*b*x^3 + 20*a^3)/x^21

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Sympy [A]  time = 2.30862, size = 39, normalized size = 0.91 \[ - \frac{20 a^{3} + 70 a^{2} b x^{3} + 84 a b^{2} x^{6} + 35 b^{3} x^{9}}{420 x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**3/x**22,x)

[Out]

-(20*a**3 + 70*a**2*b*x**3 + 84*a*b**2*x**6 + 35*b**3*x**9)/(420*x**21)

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GIAC/XCAS [A]  time = 0.215303, size = 50, normalized size = 1.16 \[ -\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^3/x^22,x, algorithm="giac")

[Out]

-1/420*(35*b^3*x^9 + 84*a*b^2*x^6 + 70*a^2*b*x^3 + 20*a^3)/x^21