Optimal. Leaf size=28 \[ -\frac{1-5 a x}{120 a^3 (1-a x)^{15} (a x+1)^{10}} \]
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Rubi [A] time = 0.0334248, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ -\frac{1-5 a x}{120 a^3 (1-a x)^{15} (a x+1)^{10}} \]
Antiderivative was successfully verified.
[In] Int[x^2/((1 - a*x)^16*(1 + a*x)^11),x]
[Out]
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Rubi in Sympy [A] time = 4.25312, size = 26, normalized size = 0.93 \[ - \frac{- 25 a x + 5}{600 a^{3} \left (- a x + 1\right )^{15} \left (a x + 1\right )^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(-a*x+1)**16/(a*x+1)**11,x)
[Out]
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Mathematica [A] time = 0.0772151, size = 27, normalized size = 0.96 \[ \frac{1-5 a x}{120 a^3 (a x-1)^{15} (a x+1)^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/((1 - a*x)^16*(1 + a*x)^11),x]
[Out]
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Maple [B] time = 0.033, size = 290, normalized size = 10.4 \[ -{\frac{1}{30720\,{a}^{3} \left ( ax-1 \right ) ^{15}}}+{\frac{1}{8192\,{a}^{3} \left ( ax-1 \right ) ^{14}}}+{\frac{11}{32768\,{a}^{3} \left ( ax-1 \right ) ^{12}}}-{\frac{11}{32768\,{a}^{3} \left ( ax-1 \right ) ^{11}}}+{\frac{143}{655360\,{a}^{3} \left ( ax-1 \right ) ^{10}}}+{\frac{143}{262144\,{a}^{3} \left ( ax-1 \right ) ^{7}}}-{\frac{2431}{3145728\,{a}^{3} \left ( ax-1 \right ) ^{6}}}+{\frac{2431}{2621440\,{a}^{3} \left ( ax-1 \right ) ^{5}}}+{\frac{4199}{4194304\,{a}^{3} \left ( ax-1 \right ) ^{3}}}-{\frac{15827}{16777216\,{a}^{3} \left ( ax-1 \right ) ^{2}}}+{\frac{3553}{4194304\,{a}^{3} \left ( ax-1 \right ) }}-{\frac{1}{4096\,{a}^{3} \left ( ax-1 \right ) ^{13}}}-{\frac{143}{524288\,{a}^{3} \left ( ax-1 \right ) ^{8}}}-{\frac{4199}{4194304\,{a}^{3} \left ( ax-1 \right ) ^{4}}}-{\frac{1}{655360\,{a}^{3} \left ( ax+1 \right ) ^{10}}}-{\frac{1}{98304\,{a}^{3} \left ( ax+1 \right ) ^{9}}}-{\frac{3}{32768\,{a}^{3} \left ( ax+1 \right ) ^{7}}}-{\frac{289}{1572864\,{a}^{3} \left ( ax+1 \right ) ^{6}}}-{\frac{51}{163840\,{a}^{3} \left ( ax+1 \right ) ^{5}}}-{\frac{323}{524288\,{a}^{3} \left ( ax+1 \right ) ^{3}}}-{\frac{12597}{16777216\,{a}^{3} \left ( ax+1 \right ) ^{2}}}-{\frac{19}{524288\,{a}^{3} \left ( ax+1 \right ) ^{8}}}-{\frac{969}{2097152\,{a}^{3} \left ( ax+1 \right ) ^{4}}}-{\frac{3553}{4194304\,{a}^{3} \left ( ax+1 \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(-a*x+1)^16/(a*x+1)^11,x)
[Out]
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Maxima [A] time = 1.47322, size = 266, normalized size = 9.5 \[ -\frac{5 \, a x - 1}{120 \,{\left (a^{28} x^{25} - 5 \, a^{27} x^{24} + 40 \, a^{25} x^{22} - 50 \, a^{24} x^{21} - 126 \, a^{23} x^{20} + 280 \, a^{22} x^{19} + 160 \, a^{21} x^{18} - 765 \, a^{20} x^{17} + 105 \, a^{19} x^{16} + 1248 \, a^{18} x^{15} - 720 \, a^{17} x^{14} - 1260 \, a^{16} x^{13} + 1260 \, a^{15} x^{12} + 720 \, a^{14} x^{11} - 1248 \, a^{13} x^{10} - 105 \, a^{12} x^{9} + 765 \, a^{11} x^{8} - 160 \, a^{10} x^{7} - 280 \, a^{9} x^{6} + 126 \, a^{8} x^{5} + 50 \, a^{7} x^{4} - 40 \, a^{6} x^{3} + 5 \, a^{4} x - a^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((a*x + 1)^11*(a*x - 1)^16),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.326674, size = 266, normalized size = 9.5 \[ -\frac{5 \, a x - 1}{120 \,{\left (a^{28} x^{25} - 5 \, a^{27} x^{24} + 40 \, a^{25} x^{22} - 50 \, a^{24} x^{21} - 126 \, a^{23} x^{20} + 280 \, a^{22} x^{19} + 160 \, a^{21} x^{18} - 765 \, a^{20} x^{17} + 105 \, a^{19} x^{16} + 1248 \, a^{18} x^{15} - 720 \, a^{17} x^{14} - 1260 \, a^{16} x^{13} + 1260 \, a^{15} x^{12} + 720 \, a^{14} x^{11} - 1248 \, a^{13} x^{10} - 105 \, a^{12} x^{9} + 765 \, a^{11} x^{8} - 160 \, a^{10} x^{7} - 280 \, a^{9} x^{6} + 126 \, a^{8} x^{5} + 50 \, a^{7} x^{4} - 40 \, a^{6} x^{3} + 5 \, a^{4} x - a^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((a*x + 1)^11*(a*x - 1)^16),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(x**2/(-a*x+1)**16/(a*x+1)**11,x)
[Out]
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GIAC/XCAS [A] time = 0.219872, size = 277, normalized size = 9.89 \[ -\frac{213180 \, a^{9} x^{9} + 2107575 \, a^{8} x^{8} + 9341160 \, a^{7} x^{7} + 24399420 \, a^{6} x^{6} + 41474016 \, a^{5} x^{5} + 47696050 \, a^{4} x^{4} + 37231960 \, a^{3} x^{3} + 19104300 \, a^{2} x^{2} + 5879780 \, a x + 833135}{251658240 \,{\left (a x + 1\right )}^{10} a^{3}} + \frac{213180 \, a^{14} x^{14} - 3221925 \, a^{13} x^{13} + 22737585 \, a^{12} x^{12} - 99390330 \, a^{11} x^{11} + 300923766 \, a^{10} x^{10} - 668342675 \, a^{9} x^{9} + 1124389695 \, a^{8} x^{8} - 1457870700 \, a^{7} x^{7} + 1466424960 \, a^{6} x^{6} - 1140648795 \, a^{5} x^{5} + 676154655 \, a^{4} x^{4} - 295952250 \, a^{3} x^{3} + 89819310 \, a^{2} x^{2} - 16508685 \, a x + 1264017}{251658240 \,{\left (a x - 1\right )}^{15} a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((a*x + 1)^11*(a*x - 1)^16),x, algorithm="giac")
[Out]