Optimal. Leaf size=217 \[ -\frac{55 b^2 \log \left (a+b x^2\right )}{2 a^{12}}+\frac{55 b^2 \log (x)}{a^{12}}+\frac{45 b^2}{2 a^{11} \left (a+b x^2\right )}+\frac{5 b}{a^{11} x^2}+\frac{9 b^2}{a^{10} \left (a+b x^2\right )^2}-\frac{1}{4 a^{10} x^4}+\frac{14 b^2}{3 a^9 \left (a+b x^2\right )^3}+\frac{21 b^2}{8 a^8 \left (a+b x^2\right )^4}+\frac{3 b^2}{2 a^7 \left (a+b x^2\right )^5}+\frac{5 b^2}{6 a^6 \left (a+b x^2\right )^6}+\frac{3 b^2}{7 a^5 \left (a+b x^2\right )^7}+\frac{3 b^2}{16 a^4 \left (a+b x^2\right )^8}+\frac{b^2}{18 a^3 \left (a+b x^2\right )^9} \]
[Out]
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Rubi [A] time = 0.485105, antiderivative size = 217, 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 \[ -\frac{55 b^2 \log \left (a+b x^2\right )}{2 a^{12}}+\frac{55 b^2 \log (x)}{a^{12}}+\frac{45 b^2}{2 a^{11} \left (a+b x^2\right )}+\frac{5 b}{a^{11} x^2}+\frac{9 b^2}{a^{10} \left (a+b x^2\right )^2}-\frac{1}{4 a^{10} x^4}+\frac{14 b^2}{3 a^9 \left (a+b x^2\right )^3}+\frac{21 b^2}{8 a^8 \left (a+b x^2\right )^4}+\frac{3 b^2}{2 a^7 \left (a+b x^2\right )^5}+\frac{5 b^2}{6 a^6 \left (a+b x^2\right )^6}+\frac{3 b^2}{7 a^5 \left (a+b x^2\right )^7}+\frac{3 b^2}{16 a^4 \left (a+b x^2\right )^8}+\frac{b^2}{18 a^3 \left (a+b x^2\right )^9} \]
Antiderivative was successfully verified.
[In] Int[1/(x^5*(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**5/(b*x**2+a)**10,x)
[Out]
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Mathematica [A] time = 0.18622, size = 151, normalized size = 0.7 \[ \frac{\frac{a \left (-252 a^{10}+2772 a^9 b x^2+78419 a^8 b^2 x^4+456291 a^7 b^3 x^6+1326204 a^6 b^4 x^8+2318316 a^5 b^5 x^{10}+2604294 a^4 b^6 x^{12}+1905750 a^3 b^7 x^{14}+882420 a^2 b^8 x^{16}+235620 a b^9 x^{18}+27720 b^{10} x^{20}\right )}{x^4 \left (a+b x^2\right )^9}-27720 b^2 \log \left (a+b x^2\right )+55440 b^2 \log (x)}{1008 a^{12}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^5*(a + b*x^2)^10),x]
[Out]
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Maple [A] time = 0.029, size = 198, normalized size = 0.9 \[ -{\frac{1}{4\,{a}^{10}{x}^{4}}}+5\,{\frac{b}{{a}^{11}{x}^{2}}}+{\frac{{b}^{2}}{18\,{a}^{3} \left ( b{x}^{2}+a \right ) ^{9}}}+{\frac{3\,{b}^{2}}{16\,{a}^{4} \left ( b{x}^{2}+a \right ) ^{8}}}+{\frac{3\,{b}^{2}}{7\,{a}^{5} \left ( b{x}^{2}+a \right ) ^{7}}}+{\frac{5\,{b}^{2}}{6\,{a}^{6} \left ( b{x}^{2}+a \right ) ^{6}}}+{\frac{3\,{b}^{2}}{2\,{a}^{7} \left ( b{x}^{2}+a \right ) ^{5}}}+{\frac{21\,{b}^{2}}{8\,{a}^{8} \left ( b{x}^{2}+a \right ) ^{4}}}+{\frac{14\,{b}^{2}}{3\,{a}^{9} \left ( b{x}^{2}+a \right ) ^{3}}}+9\,{\frac{{b}^{2}}{{a}^{10} \left ( b{x}^{2}+a \right ) ^{2}}}+{\frac{45\,{b}^{2}}{2\,{a}^{11} \left ( b{x}^{2}+a \right ) }}+55\,{\frac{{b}^{2}\ln \left ( x \right ) }{{a}^{12}}}-{\frac{55\,{b}^{2}\ln \left ( b{x}^{2}+a \right ) }{2\,{a}^{12}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^5/(b*x^2+a)^10,x)
[Out]
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Maxima [A] time = 1.37607, size = 332, normalized size = 1.53 \[ \frac{27720 \, b^{10} x^{20} + 235620 \, a b^{9} x^{18} + 882420 \, a^{2} b^{8} x^{16} + 1905750 \, a^{3} b^{7} x^{14} + 2604294 \, a^{4} b^{6} x^{12} + 2318316 \, a^{5} b^{5} x^{10} + 1326204 \, a^{6} b^{4} x^{8} + 456291 \, a^{7} b^{3} x^{6} + 78419 \, a^{8} b^{2} x^{4} + 2772 \, a^{9} b x^{2} - 252 \, a^{10}}{1008 \,{\left (a^{11} b^{9} x^{22} + 9 \, a^{12} b^{8} x^{20} + 36 \, a^{13} b^{7} x^{18} + 84 \, a^{14} b^{6} x^{16} + 126 \, a^{15} b^{5} x^{14} + 126 \, a^{16} b^{4} x^{12} + 84 \, a^{17} b^{3} x^{10} + 36 \, a^{18} b^{2} x^{8} + 9 \, a^{19} b x^{6} + a^{20} x^{4}\right )}} - \frac{55 \, b^{2} \log \left (b x^{2} + a\right )}{2 \, a^{12}} + \frac{55 \, b^{2} \log \left (x^{2}\right )}{2 \, a^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)^10*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231136, size = 597, normalized size = 2.75 \[ \frac{27720 \, a b^{10} x^{20} + 235620 \, a^{2} b^{9} x^{18} + 882420 \, a^{3} b^{8} x^{16} + 1905750 \, a^{4} b^{7} x^{14} + 2604294 \, a^{5} b^{6} x^{12} + 2318316 \, a^{6} b^{5} x^{10} + 1326204 \, a^{7} b^{4} x^{8} + 456291 \, a^{8} b^{3} x^{6} + 78419 \, a^{9} b^{2} x^{4} + 2772 \, a^{10} b x^{2} - 252 \, a^{11} - 27720 \,{\left (b^{11} x^{22} + 9 \, a b^{10} x^{20} + 36 \, a^{2} b^{9} x^{18} + 84 \, a^{3} b^{8} x^{16} + 126 \, a^{4} b^{7} x^{14} + 126 \, a^{5} b^{6} x^{12} + 84 \, a^{6} b^{5} x^{10} + 36 \, a^{7} b^{4} x^{8} + 9 \, a^{8} b^{3} x^{6} + a^{9} b^{2} x^{4}\right )} \log \left (b x^{2} + a\right ) + 55440 \,{\left (b^{11} x^{22} + 9 \, a b^{10} x^{20} + 36 \, a^{2} b^{9} x^{18} + 84 \, a^{3} b^{8} x^{16} + 126 \, a^{4} b^{7} x^{14} + 126 \, a^{5} b^{6} x^{12} + 84 \, a^{6} b^{5} x^{10} + 36 \, a^{7} b^{4} x^{8} + 9 \, a^{8} b^{3} x^{6} + a^{9} b^{2} x^{4}\right )} \log \left (x\right )}{1008 \,{\left (a^{12} b^{9} x^{22} + 9 \, a^{13} b^{8} x^{20} + 36 \, a^{14} b^{7} x^{18} + 84 \, a^{15} b^{6} x^{16} + 126 \, a^{16} b^{5} x^{14} + 126 \, a^{17} b^{4} x^{12} + 84 \, a^{18} b^{3} x^{10} + 36 \, a^{19} b^{2} x^{8} + 9 \, a^{20} b x^{6} + a^{21} x^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)^10*x^5),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**5/(b*x**2+a)**10,x)
[Out]
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GIAC/XCAS [A] time = 0.214434, size = 235, normalized size = 1.08 \[ \frac{55 \, b^{2}{\rm ln}\left (x^{2}\right )}{2 \, a^{12}} - \frac{55 \, b^{2}{\rm ln}\left ({\left | b x^{2} + a \right |}\right )}{2 \, a^{12}} - \frac{165 \, b^{2} x^{4} - 20 \, a b x^{2} + a^{2}}{4 \, a^{12} x^{4}} + \frac{78419 \, b^{11} x^{18} + 728451 \, a b^{10} x^{16} + 3013596 \, a^{2} b^{9} x^{14} + 7290444 \, a^{3} b^{8} x^{12} + 11372256 \, a^{4} b^{7} x^{10} + 11871216 \, a^{5} b^{6} x^{8} + 8302224 \, a^{6} b^{5} x^{6} + 3757680 \, a^{7} b^{4} x^{4} + 1001790 \, a^{8} b^{3} x^{2} + 120550 \, a^{9} b^{2}}{1008 \,{\left (b x^{2} + a\right )}^{9} a^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)^10*x^5),x, algorithm="giac")
[Out]