3.273 \(\int \frac{\left (a+b x^3\right )^5}{x^{28}} \, dx\)

Optimal. Leaf size=69 \[ -\frac{a^5}{27 x^{27}}-\frac{5 a^4 b}{24 x^{24}}-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}} \]

[Out]

-a^5/(27*x^27) - (5*a^4*b)/(24*x^24) - (10*a^3*b^2)/(21*x^21) - (5*a^2*b^3)/(9*x
^18) - (a*b^4)/(3*x^15) - b^5/(12*x^12)

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Rubi [A]  time = 0.0801097, antiderivative size = 69, 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 \[ -\frac{a^5}{27 x^{27}}-\frac{5 a^4 b}{24 x^{24}}-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^5/x^28,x]

[Out]

-a^5/(27*x^27) - (5*a^4*b)/(24*x^24) - (10*a^3*b^2)/(21*x^21) - (5*a^2*b^3)/(9*x
^18) - (a*b^4)/(3*x^15) - b^5/(12*x^12)

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Rubi in Sympy [A]  time = 13.9344, size = 66, normalized size = 0.96 \[ - \frac{a^{5}}{27 x^{27}} - \frac{5 a^{4} b}{24 x^{24}} - \frac{10 a^{3} b^{2}}{21 x^{21}} - \frac{5 a^{2} b^{3}}{9 x^{18}} - \frac{a b^{4}}{3 x^{15}} - \frac{b^{5}}{12 x^{12}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**5/x**28,x)

[Out]

-a**5/(27*x**27) - 5*a**4*b/(24*x**24) - 10*a**3*b**2/(21*x**21) - 5*a**2*b**3/(
9*x**18) - a*b**4/(3*x**15) - b**5/(12*x**12)

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Mathematica [A]  time = 0.00780375, size = 69, normalized size = 1. \[ -\frac{a^5}{27 x^{27}}-\frac{5 a^4 b}{24 x^{24}}-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^5/x^28,x]

[Out]

-a^5/(27*x^27) - (5*a^4*b)/(24*x^24) - (10*a^3*b^2)/(21*x^21) - (5*a^2*b^3)/(9*x
^18) - (a*b^4)/(3*x^15) - b^5/(12*x^12)

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Maple [A]  time = 0.008, size = 58, normalized size = 0.8 \[ -{\frac{{a}^{5}}{27\,{x}^{27}}}-{\frac{5\,{a}^{4}b}{24\,{x}^{24}}}-{\frac{10\,{a}^{3}{b}^{2}}{21\,{x}^{21}}}-{\frac{5\,{a}^{2}{b}^{3}}{9\,{x}^{18}}}-{\frac{a{b}^{4}}{3\,{x}^{15}}}-{\frac{{b}^{5}}{12\,{x}^{12}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^5/x^28,x)

[Out]

-1/27*a^5/x^27-5/24*a^4*b/x^24-10/21*a^3*b^2/x^21-5/9*a^2*b^3/x^18-1/3*a*b^4/x^1
5-1/12*b^5/x^12

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Maxima [A]  time = 1.45702, size = 80, normalized size = 1.16 \[ -\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^5/x^28,x, algorithm="maxima")

[Out]

-1/1512*(126*b^5*x^15 + 504*a*b^4*x^12 + 840*a^2*b^3*x^9 + 720*a^3*b^2*x^6 + 315
*a^4*b*x^3 + 56*a^5)/x^27

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Fricas [A]  time = 0.202732, size = 80, normalized size = 1.16 \[ -\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^5/x^28,x, algorithm="fricas")

[Out]

-1/1512*(126*b^5*x^15 + 504*a*b^4*x^12 + 840*a^2*b^3*x^9 + 720*a^3*b^2*x^6 + 315
*a^4*b*x^3 + 56*a^5)/x^27

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Sympy [A]  time = 3.46091, size = 63, normalized size = 0.91 \[ - \frac{56 a^{5} + 315 a^{4} b x^{3} + 720 a^{3} b^{2} x^{6} + 840 a^{2} b^{3} x^{9} + 504 a b^{4} x^{12} + 126 b^{5} x^{15}}{1512 x^{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**5/x**28,x)

[Out]

-(56*a**5 + 315*a**4*b*x**3 + 720*a**3*b**2*x**6 + 840*a**2*b**3*x**9 + 504*a*b*
*4*x**12 + 126*b**5*x**15)/(1512*x**27)

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GIAC/XCAS [A]  time = 0.218413, size = 80, normalized size = 1.16 \[ -\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^5/x^28,x, algorithm="giac")

[Out]

-1/1512*(126*b^5*x^15 + 504*a*b^4*x^12 + 840*a^2*b^3*x^9 + 720*a^3*b^2*x^6 + 315
*a^4*b*x^3 + 56*a^5)/x^27