3.2720 \(\int \frac{\left (a+b x^3\right )^8}{x^{28}} \, dx\)

Optimal. Leaf size=19 \[ -\frac{\left (a+b x^3\right )^9}{27 a x^{27}} \]

[Out]

-(a + b*x^3)^9/(27*a*x^27)

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Rubi [A]  time = 0.0193318, 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 \[ -\frac{\left (a+b x^3\right )^9}{27 a x^{27}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^8/x^28,x]

[Out]

-(a + b*x^3)^9/(27*a*x^27)

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Rubi in Sympy [A]  time = 2.74221, size = 15, normalized size = 0.79 \[ - \frac{\left (a + b x^{3}\right )^{9}}{27 a x^{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**8/x**28,x)

[Out]

-(a + b*x**3)**9/(27*a*x**27)

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Mathematica [B]  time = 0.0144024, size = 108, normalized size = 5.68 \[ -\frac{a^8}{27 x^{27}}-\frac{a^7 b}{3 x^{24}}-\frac{4 a^6 b^2}{3 x^{21}}-\frac{28 a^5 b^3}{9 x^{18}}-\frac{14 a^4 b^4}{3 x^{15}}-\frac{14 a^3 b^5}{3 x^{12}}-\frac{28 a^2 b^6}{9 x^9}-\frac{4 a b^7}{3 x^6}-\frac{b^8}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^8/x^28,x]

[Out]

-a^8/(27*x^27) - (a^7*b)/(3*x^24) - (4*a^6*b^2)/(3*x^21) - (28*a^5*b^3)/(9*x^18)
- (14*a^4*b^4)/(3*x^15) - (14*a^3*b^5)/(3*x^12) - (28*a^2*b^6)/(9*x^9) - (4*a*b
^7)/(3*x^6) - b^8/(3*x^3)

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Maple [B]  time = 0.002, size = 91, normalized size = 4.8 \[ -{\frac{14\,{a}^{3}{b}^{5}}{3\,{x}^{12}}}-{\frac{14\,{a}^{4}{b}^{4}}{3\,{x}^{15}}}-{\frac{4\,{a}^{6}{b}^{2}}{3\,{x}^{21}}}-{\frac{28\,{a}^{5}{b}^{3}}{9\,{x}^{18}}}-{\frac{4\,a{b}^{7}}{3\,{x}^{6}}}-{\frac{b{a}^{7}}{3\,{x}^{24}}}-{\frac{28\,{a}^{2}{b}^{6}}{9\,{x}^{9}}}-{\frac{{b}^{8}}{3\,{x}^{3}}}-{\frac{{a}^{8}}{27\,{x}^{27}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^8/x^28,x)

[Out]

-14/3*a^3*b^5/x^12-14/3*a^4*b^4/x^15-4/3*a^6*b^2/x^21-28/9*a^5*b^3/x^18-4/3*a*b^
7/x^6-1/3*a^7*b/x^24-28/9*a^2*b^6/x^9-1/3*b^8/x^3-1/27*a^8/x^27

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Maxima [A]  time = 1.3448, size = 122, normalized size = 6.42 \[ -\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^8/x^28,x, algorithm="maxima")

[Out]

-1/27*(9*b^8*x^24 + 36*a*b^7*x^21 + 84*a^2*b^6*x^18 + 126*a^3*b^5*x^15 + 126*a^4
*b^4*x^12 + 84*a^5*b^3*x^9 + 36*a^6*b^2*x^6 + 9*a^7*b*x^3 + a^8)/x^27

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Fricas [A]  time = 0.206211, size = 122, normalized size = 6.42 \[ -\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^8/x^28,x, algorithm="fricas")

[Out]

-1/27*(9*b^8*x^24 + 36*a*b^7*x^21 + 84*a^2*b^6*x^18 + 126*a^3*b^5*x^15 + 126*a^4
*b^4*x^12 + 84*a^5*b^3*x^9 + 36*a^6*b^2*x^6 + 9*a^7*b*x^3 + a^8)/x^27

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Sympy [A]  time = 4.90974, size = 97, normalized size = 5.11 \[ - \frac{a^{8} + 9 a^{7} b x^{3} + 36 a^{6} b^{2} x^{6} + 84 a^{5} b^{3} x^{9} + 126 a^{4} b^{4} x^{12} + 126 a^{3} b^{5} x^{15} + 84 a^{2} b^{6} x^{18} + 36 a b^{7} x^{21} + 9 b^{8} x^{24}}{27 x^{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**8/x**28,x)

[Out]

-(a**8 + 9*a**7*b*x**3 + 36*a**6*b**2*x**6 + 84*a**5*b**3*x**9 + 126*a**4*b**4*x
**12 + 126*a**3*b**5*x**15 + 84*a**2*b**6*x**18 + 36*a*b**7*x**21 + 9*b**8*x**24
)/(27*x**27)

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GIAC/XCAS [A]  time = 0.216665, size = 122, normalized size = 6.42 \[ -\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^8/x^28,x, algorithm="giac")

[Out]

-1/27*(9*b^8*x^24 + 36*a*b^7*x^21 + 84*a^2*b^6*x^18 + 126*a^3*b^5*x^15 + 126*a^4
*b^4*x^12 + 84*a^5*b^3*x^9 + 36*a^6*b^2*x^6 + 9*a^7*b*x^3 + a^8)/x^27