Optimal. Leaf size=184 \[ \frac{5 b \log \left (a+b x^2\right )}{a^{11}}-\frac{10 b \log (x)}{a^{11}}-\frac{9 b}{2 a^{10} \left (a+b x^2\right )}-\frac{1}{2 a^{10} x^2}-\frac{2 b}{a^9 \left (a+b x^2\right )^2}-\frac{7 b}{6 a^8 \left (a+b x^2\right )^3}-\frac{3 b}{4 a^7 \left (a+b x^2\right )^4}-\frac{b}{2 a^6 \left (a+b x^2\right )^5}-\frac{b}{3 a^5 \left (a+b x^2\right )^6}-\frac{3 b}{14 a^4 \left (a+b x^2\right )^7}-\frac{b}{8 a^3 \left (a+b x^2\right )^8}-\frac{b}{18 a^2 \left (a+b x^2\right )^9} \]
[Out]
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Rubi [A] time = 0.411028, antiderivative size = 184, 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 \[ \frac{5 b \log \left (a+b x^2\right )}{a^{11}}-\frac{10 b \log (x)}{a^{11}}-\frac{9 b}{2 a^{10} \left (a+b x^2\right )}-\frac{1}{2 a^{10} x^2}-\frac{2 b}{a^9 \left (a+b x^2\right )^2}-\frac{7 b}{6 a^8 \left (a+b x^2\right )^3}-\frac{3 b}{4 a^7 \left (a+b x^2\right )^4}-\frac{b}{2 a^6 \left (a+b x^2\right )^5}-\frac{b}{3 a^5 \left (a+b x^2\right )^6}-\frac{3 b}{14 a^4 \left (a+b x^2\right )^7}-\frac{b}{8 a^3 \left (a+b x^2\right )^8}-\frac{b}{18 a^2 \left (a+b x^2\right )^9} \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*(a + b*x^2)^10),x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(b*x**2+a)**10,x)
[Out]
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Mathematica [A] time = 0.242227, size = 136, normalized size = 0.74 \[ -\frac{\frac{a \left (252 a^9+7129 a^8 b x^2+41481 a^7 b^2 x^4+120564 a^6 b^3 x^6+210756 a^5 b^4 x^8+236754 a^4 b^5 x^{10}+173250 a^3 b^6 x^{12}+80220 a^2 b^7 x^{14}+21420 a b^8 x^{16}+2520 b^9 x^{18}\right )}{x^2 \left (a+b x^2\right )^9}-2520 b \log \left (a+b x^2\right )+5040 b \log (x)}{504 a^{11}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*(a + b*x^2)^10),x]
[Out]
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Maple [A] time = 0.029, size = 167, normalized size = 0.9 \[ -{\frac{1}{2\,{a}^{10}{x}^{2}}}-{\frac{b}{18\,{a}^{2} \left ( b{x}^{2}+a \right ) ^{9}}}-{\frac{b}{8\,{a}^{3} \left ( b{x}^{2}+a \right ) ^{8}}}-{\frac{3\,b}{14\,{a}^{4} \left ( b{x}^{2}+a \right ) ^{7}}}-{\frac{b}{3\,{a}^{5} \left ( b{x}^{2}+a \right ) ^{6}}}-{\frac{b}{2\,{a}^{6} \left ( b{x}^{2}+a \right ) ^{5}}}-{\frac{3\,b}{4\,{a}^{7} \left ( b{x}^{2}+a \right ) ^{4}}}-{\frac{7\,b}{6\,{a}^{8} \left ( b{x}^{2}+a \right ) ^{3}}}-2\,{\frac{b}{{a}^{9} \left ( b{x}^{2}+a \right ) ^{2}}}-{\frac{9\,b}{2\,{a}^{10} \left ( b{x}^{2}+a \right ) }}-10\,{\frac{b\ln \left ( x \right ) }{{a}^{11}}}+5\,{\frac{b\ln \left ( b{x}^{2}+a \right ) }{{a}^{11}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(b*x^2+a)^10,x)
[Out]
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Maxima [A] time = 1.3957, size = 312, normalized size = 1.7 \[ -\frac{2520 \, b^{9} x^{18} + 21420 \, a b^{8} x^{16} + 80220 \, a^{2} b^{7} x^{14} + 173250 \, a^{3} b^{6} x^{12} + 236754 \, a^{4} b^{5} x^{10} + 210756 \, a^{5} b^{4} x^{8} + 120564 \, a^{6} b^{3} x^{6} + 41481 \, a^{7} b^{2} x^{4} + 7129 \, a^{8} b x^{2} + 252 \, a^{9}}{504 \,{\left (a^{10} b^{9} x^{20} + 9 \, a^{11} b^{8} x^{18} + 36 \, a^{12} b^{7} x^{16} + 84 \, a^{13} b^{6} x^{14} + 126 \, a^{14} b^{5} x^{12} + 126 \, a^{15} b^{4} x^{10} + 84 \, a^{16} b^{3} x^{8} + 36 \, a^{17} b^{2} x^{6} + 9 \, a^{18} b x^{4} + a^{19} x^{2}\right )}} + \frac{5 \, b \log \left (b x^{2} + a\right )}{a^{11}} - \frac{5 \, b \log \left (x^{2}\right )}{a^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)^10*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240893, size = 576, normalized size = 3.13 \[ -\frac{2520 \, a b^{9} x^{18} + 21420 \, a^{2} b^{8} x^{16} + 80220 \, a^{3} b^{7} x^{14} + 173250 \, a^{4} b^{6} x^{12} + 236754 \, a^{5} b^{5} x^{10} + 210756 \, a^{6} b^{4} x^{8} + 120564 \, a^{7} b^{3} x^{6} + 41481 \, a^{8} b^{2} x^{4} + 7129 \, a^{9} b x^{2} + 252 \, a^{10} - 2520 \,{\left (b^{10} x^{20} + 9 \, a b^{9} x^{18} + 36 \, a^{2} b^{8} x^{16} + 84 \, a^{3} b^{7} x^{14} + 126 \, a^{4} b^{6} x^{12} + 126 \, a^{5} b^{5} x^{10} + 84 \, a^{6} b^{4} x^{8} + 36 \, a^{7} b^{3} x^{6} + 9 \, a^{8} b^{2} x^{4} + a^{9} b x^{2}\right )} \log \left (b x^{2} + a\right ) + 5040 \,{\left (b^{10} x^{20} + 9 \, a b^{9} x^{18} + 36 \, a^{2} b^{8} x^{16} + 84 \, a^{3} b^{7} x^{14} + 126 \, a^{4} b^{6} x^{12} + 126 \, a^{5} b^{5} x^{10} + 84 \, a^{6} b^{4} x^{8} + 36 \, a^{7} b^{3} x^{6} + 9 \, a^{8} b^{2} x^{4} + a^{9} b x^{2}\right )} \log \left (x\right )}{504 \,{\left (a^{11} b^{9} x^{20} + 9 \, a^{12} b^{8} x^{18} + 36 \, a^{13} b^{7} x^{16} + 84 \, a^{14} b^{6} x^{14} + 126 \, a^{15} b^{5} x^{12} + 126 \, a^{16} b^{4} x^{10} + 84 \, a^{17} b^{3} x^{8} + 36 \, a^{18} b^{2} x^{6} + 9 \, a^{19} b x^{4} + a^{20} x^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)^10*x^3),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(1/x**3/(b*x**2+a)**10,x)
[Out]
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GIAC/XCAS [A] time = 0.217368, size = 215, normalized size = 1.17 \[ -\frac{5 \, b{\rm ln}\left (x^{2}\right )}{a^{11}} + \frac{5 \, b{\rm ln}\left ({\left | b x^{2} + a \right |}\right )}{a^{11}} + \frac{10 \, b x^{2} - a}{2 \, a^{11} x^{2}} - \frac{7129 \, b^{10} x^{18} + 66429 \, a b^{9} x^{16} + 275796 \, a^{2} b^{8} x^{14} + 669984 \, a^{3} b^{7} x^{12} + 1050336 \, a^{4} b^{6} x^{10} + 1103256 \, a^{5} b^{5} x^{8} + 777840 \, a^{6} b^{4} x^{6} + 356040 \, a^{7} b^{3} x^{4} + 96570 \, a^{8} b^{2} x^{2} + 11990 \, a^{9} b}{504 \,{\left (b x^{2} + a\right )}^{9} a^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)^10*x^3),x, algorithm="giac")
[Out]