3.83 \(\int \frac{\left (a+b x^2\right )^5}{x^{18}} \, dx\)

Optimal. Leaf size=69 \[ -\frac{a^5}{17 x^{17}}-\frac{a^4 b}{3 x^{15}}-\frac{10 a^3 b^2}{13 x^{13}}-\frac{10 a^2 b^3}{11 x^{11}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{7 x^7} \]

[Out]

-a^5/(17*x^17) - (a^4*b)/(3*x^15) - (10*a^3*b^2)/(13*x^13) - (10*a^2*b^3)/(11*x^
11) - (5*a*b^4)/(9*x^9) - b^5/(7*x^7)

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Rubi [A]  time = 0.065953, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^5}{17 x^{17}}-\frac{a^4 b}{3 x^{15}}-\frac{10 a^3 b^2}{13 x^{13}}-\frac{10 a^2 b^3}{11 x^{11}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{7 x^7} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^2)^5/x^18,x]

[Out]

-a^5/(17*x^17) - (a^4*b)/(3*x^15) - (10*a^3*b^2)/(13*x^13) - (10*a^2*b^3)/(11*x^
11) - (5*a*b^4)/(9*x^9) - b^5/(7*x^7)

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Rubi in Sympy [A]  time = 12.6108, size = 66, normalized size = 0.96 \[ - \frac{a^{5}}{17 x^{17}} - \frac{a^{4} b}{3 x^{15}} - \frac{10 a^{3} b^{2}}{13 x^{13}} - \frac{10 a^{2} b^{3}}{11 x^{11}} - \frac{5 a b^{4}}{9 x^{9}} - \frac{b^{5}}{7 x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2+a)**5/x**18,x)

[Out]

-a**5/(17*x**17) - a**4*b/(3*x**15) - 10*a**3*b**2/(13*x**13) - 10*a**2*b**3/(11
*x**11) - 5*a*b**4/(9*x**9) - b**5/(7*x**7)

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Mathematica [A]  time = 0.00769079, size = 69, normalized size = 1. \[ -\frac{a^5}{17 x^{17}}-\frac{a^4 b}{3 x^{15}}-\frac{10 a^3 b^2}{13 x^{13}}-\frac{10 a^2 b^3}{11 x^{11}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{7 x^7} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^2)^5/x^18,x]

[Out]

-a^5/(17*x^17) - (a^4*b)/(3*x^15) - (10*a^3*b^2)/(13*x^13) - (10*a^2*b^3)/(11*x^
11) - (5*a*b^4)/(9*x^9) - b^5/(7*x^7)

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Maple [A]  time = 0.008, size = 58, normalized size = 0.8 \[ -{\frac{{a}^{5}}{17\,{x}^{17}}}-{\frac{{a}^{4}b}{3\,{x}^{15}}}-{\frac{10\,{a}^{3}{b}^{2}}{13\,{x}^{13}}}-{\frac{10\,{a}^{2}{b}^{3}}{11\,{x}^{11}}}-{\frac{5\,a{b}^{4}}{9\,{x}^{9}}}-{\frac{{b}^{5}}{7\,{x}^{7}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2+a)^5/x^18,x)

[Out]

-1/17*a^5/x^17-1/3*a^4*b/x^15-10/13*a^3*b^2/x^13-10/11*a^2*b^3/x^11-5/9*a*b^4/x^
9-1/7*b^5/x^7

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Maxima [A]  time = 1.34645, size = 80, normalized size = 1.16 \[ -\frac{21879 \, b^{5} x^{10} + 85085 \, a b^{4} x^{8} + 139230 \, a^{2} b^{3} x^{6} + 117810 \, a^{3} b^{2} x^{4} + 51051 \, a^{4} b x^{2} + 9009 \, a^{5}}{153153 \, x^{17}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2 + a)^5/x^18,x, algorithm="maxima")

[Out]

-1/153153*(21879*b^5*x^10 + 85085*a*b^4*x^8 + 139230*a^2*b^3*x^6 + 117810*a^3*b^
2*x^4 + 51051*a^4*b*x^2 + 9009*a^5)/x^17

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Fricas [A]  time = 0.193724, size = 80, normalized size = 1.16 \[ -\frac{21879 \, b^{5} x^{10} + 85085 \, a b^{4} x^{8} + 139230 \, a^{2} b^{3} x^{6} + 117810 \, a^{3} b^{2} x^{4} + 51051 \, a^{4} b x^{2} + 9009 \, a^{5}}{153153 \, x^{17}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2 + a)^5/x^18,x, algorithm="fricas")

[Out]

-1/153153*(21879*b^5*x^10 + 85085*a*b^4*x^8 + 139230*a^2*b^3*x^6 + 117810*a^3*b^
2*x^4 + 51051*a^4*b*x^2 + 9009*a^5)/x^17

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Sympy [A]  time = 2.63696, size = 63, normalized size = 0.91 \[ - \frac{9009 a^{5} + 51051 a^{4} b x^{2} + 117810 a^{3} b^{2} x^{4} + 139230 a^{2} b^{3} x^{6} + 85085 a b^{4} x^{8} + 21879 b^{5} x^{10}}{153153 x^{17}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2+a)**5/x**18,x)

[Out]

-(9009*a**5 + 51051*a**4*b*x**2 + 117810*a**3*b**2*x**4 + 139230*a**2*b**3*x**6
+ 85085*a*b**4*x**8 + 21879*b**5*x**10)/(153153*x**17)

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GIAC/XCAS [A]  time = 0.211336, size = 80, normalized size = 1.16 \[ -\frac{21879 \, b^{5} x^{10} + 85085 \, a b^{4} x^{8} + 139230 \, a^{2} b^{3} x^{6} + 117810 \, a^{3} b^{2} x^{4} + 51051 \, a^{4} b x^{2} + 9009 \, a^{5}}{153153 \, x^{17}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2 + a)^5/x^18,x, algorithm="giac")

[Out]

-1/153153*(21879*b^5*x^10 + 85085*a*b^4*x^8 + 139230*a^2*b^3*x^6 + 117810*a^3*b^
2*x^4 + 51051*a^4*b*x^2 + 9009*a^5)/x^17