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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]