Optimal. Leaf size=117 \[ -\frac{a^5 A}{19 x^{19}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{a^3 b (a B+2 A b)}{3 x^{15}}-\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{b^4 (5 a B+A b)}{9 x^9}-\frac{5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac{b^5 B}{7 x^7} \]
[Out]
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Rubi [A] time = 0.196816, antiderivative size = 117, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{a^5 A}{19 x^{19}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{a^3 b (a B+2 A b)}{3 x^{15}}-\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{b^4 (5 a B+A b)}{9 x^9}-\frac{5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac{b^5 B}{7 x^7} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)^5*(A + B*x^2))/x^20,x]
[Out]
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Rubi in Sympy [A] time = 24.5347, size = 114, normalized size = 0.97 \[ - \frac{A a^{5}}{19 x^{19}} - \frac{B b^{5}}{7 x^{7}} - \frac{a^{4} \left (5 A b + B a\right )}{17 x^{17}} - \frac{a^{3} b \left (2 A b + B a\right )}{3 x^{15}} - \frac{10 a^{2} b^{2} \left (A b + B a\right )}{13 x^{13}} - \frac{5 a b^{3} \left (A b + 2 B a\right )}{11 x^{11}} - \frac{b^{4} \left (A b + 5 B a\right )}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**5*(B*x**2+A)/x**20,x)
[Out]
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Mathematica [A] time = 0.0951047, size = 117, normalized size = 1. \[ -\frac{a^5 A}{19 x^{19}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{a^3 b (a B+2 A b)}{3 x^{15}}-\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{b^4 (5 a B+A b)}{9 x^9}-\frac{5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac{b^5 B}{7 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)^5*(A + B*x^2))/x^20,x]
[Out]
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Maple [A] time = 0.008, size = 104, normalized size = 0.9 \[ -{\frac{A{a}^{5}}{19\,{x}^{19}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{17\,{x}^{17}}}-{\frac{{a}^{3}b \left ( 2\,Ab+Ba \right ) }{3\,{x}^{15}}}-{\frac{10\,{a}^{2}{b}^{2} \left ( Ab+Ba \right ) }{13\,{x}^{13}}}-{\frac{5\,a{b}^{3} \left ( Ab+2\,Ba \right ) }{11\,{x}^{11}}}-{\frac{{b}^{4} \left ( Ab+5\,Ba \right ) }{9\,{x}^{9}}}-{\frac{B{b}^{5}}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^5*(B*x^2+A)/x^20,x)
[Out]
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Maxima [A] time = 1.37749, size = 163, normalized size = 1.39 \[ -\frac{415701 \, B b^{5} x^{12} + 323323 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 1322685 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 2238390 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 153153 \, A a^{5} + 969969 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 171171 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{2909907 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5/x^20,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203638, size = 163, normalized size = 1.39 \[ -\frac{415701 \, B b^{5} x^{12} + 323323 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 1322685 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 2238390 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 153153 \, A a^{5} + 969969 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 171171 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{2909907 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5/x^20,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**5*(B*x**2+A)/x**20,x)
[Out]
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GIAC/XCAS [A] time = 0.238862, size = 171, normalized size = 1.46 \[ -\frac{415701 \, B b^{5} x^{12} + 1616615 \, B a b^{4} x^{10} + 323323 \, A b^{5} x^{10} + 2645370 \, B a^{2} b^{3} x^{8} + 1322685 \, A a b^{4} x^{8} + 2238390 \, B a^{3} b^{2} x^{6} + 2238390 \, A a^{2} b^{3} x^{6} + 969969 \, B a^{4} b x^{4} + 1939938 \, A a^{3} b^{2} x^{4} + 171171 \, B a^{5} x^{2} + 855855 \, A a^{4} b x^{2} + 153153 \, A a^{5}}{2909907 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5/x^20,x, algorithm="giac")
[Out]