3.270 \(\int \frac{\left (a+b x^3\right )^5}{x^{19}} \, dx\)

Optimal. Leaf size=19 \[ -\frac{\left (a+b x^3\right )^6}{18 a x^{18}} \]

[Out]

-(a + b*x^3)^6/(18*a*x^18)

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Rubi [A]  time = 0.0163713, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{\left (a+b x^3\right )^6}{18 a x^{18}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^5/x^19,x]

[Out]

-(a + b*x^3)^6/(18*a*x^18)

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Rubi in Sympy [A]  time = 2.7323, size = 15, normalized size = 0.79 \[ - \frac{\left (a + b x^{3}\right )^{6}}{18 a x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**5/x**19,x)

[Out]

-(a + b*x**3)**6/(18*a*x**18)

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Mathematica [B]  time = 0.00793846, size = 69, normalized size = 3.63 \[ -\frac{a^5}{18 x^{18}}-\frac{a^4 b}{3 x^{15}}-\frac{5 a^3 b^2}{6 x^{12}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^5/x^19,x]

[Out]

-a^5/(18*x^18) - (a^4*b)/(3*x^15) - (5*a^3*b^2)/(6*x^12) - (10*a^2*b^3)/(9*x^9)
- (5*a*b^4)/(6*x^6) - b^5/(3*x^3)

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Maple [B]  time = 0.009, size = 58, normalized size = 3.1 \[ -{\frac{5\,{a}^{3}{b}^{2}}{6\,{x}^{12}}}-{\frac{{a}^{4}b}{3\,{x}^{15}}}-{\frac{5\,a{b}^{4}}{6\,{x}^{6}}}-{\frac{10\,{a}^{2}{b}^{3}}{9\,{x}^{9}}}-{\frac{{b}^{5}}{3\,{x}^{3}}}-{\frac{{a}^{5}}{18\,{x}^{18}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^5/x^19,x)

[Out]

-5/6*a^3*b^2/x^12-1/3*a^4*b/x^15-5/6*a*b^4/x^6-10/9*a^2*b^3/x^9-1/3*b^5/x^3-1/18
*a^5/x^18

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Maxima [A]  time = 1.42936, size = 77, normalized size = 4.05 \[ -\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^5/x^19,x, algorithm="maxima")

[Out]

-1/18*(6*b^5*x^15 + 15*a*b^4*x^12 + 20*a^2*b^3*x^9 + 15*a^3*b^2*x^6 + 6*a^4*b*x^
3 + a^5)/x^18

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Fricas [A]  time = 0.20435, size = 77, normalized size = 4.05 \[ -\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^5/x^19,x, algorithm="fricas")

[Out]

-1/18*(6*b^5*x^15 + 15*a*b^4*x^12 + 20*a^2*b^3*x^9 + 15*a^3*b^2*x^6 + 6*a^4*b*x^
3 + a^5)/x^18

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Sympy [A]  time = 2.86197, size = 61, normalized size = 3.21 \[ - \frac{a^{5} + 6 a^{4} b x^{3} + 15 a^{3} b^{2} x^{6} + 20 a^{2} b^{3} x^{9} + 15 a b^{4} x^{12} + 6 b^{5} x^{15}}{18 x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**5/x**19,x)

[Out]

-(a**5 + 6*a**4*b*x**3 + 15*a**3*b**2*x**6 + 20*a**2*b**3*x**9 + 15*a*b**4*x**12
+ 6*b**5*x**15)/(18*x**18)

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GIAC/XCAS [A]  time = 0.220862, size = 77, normalized size = 4.05 \[ -\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^5/x^19,x, algorithm="giac")

[Out]

-1/18*(6*b^5*x^15 + 15*a*b^4*x^12 + 20*a^2*b^3*x^9 + 15*a^3*b^2*x^6 + 6*a^4*b*x^
3 + a^5)/x^18