Optimal. Leaf size=186 \[ -\frac{a^{12}}{9 b^{13} (a+b x)^9}+\frac{3 a^{11}}{2 b^{13} (a+b x)^8}-\frac{66 a^{10}}{7 b^{13} (a+b x)^7}+\frac{110 a^9}{3 b^{13} (a+b x)^6}-\frac{99 a^8}{b^{13} (a+b x)^5}+\frac{198 a^7}{b^{13} (a+b x)^4}-\frac{308 a^6}{b^{13} (a+b x)^3}+\frac{396 a^5}{b^{13} (a+b x)^2}-\frac{495 a^4}{b^{13} (a+b x)}-\frac{220 a^3 \log (a+b x)}{b^{13}}+\frac{55 a^2 x}{b^{12}}-\frac{5 a x^2}{b^{11}}+\frac{x^3}{3 b^{10}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.355149, antiderivative size = 186, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a^{12}}{9 b^{13} (a+b x)^9}+\frac{3 a^{11}}{2 b^{13} (a+b x)^8}-\frac{66 a^{10}}{7 b^{13} (a+b x)^7}+\frac{110 a^9}{3 b^{13} (a+b x)^6}-\frac{99 a^8}{b^{13} (a+b x)^5}+\frac{198 a^7}{b^{13} (a+b x)^4}-\frac{308 a^6}{b^{13} (a+b x)^3}+\frac{396 a^5}{b^{13} (a+b x)^2}-\frac{495 a^4}{b^{13} (a+b x)}-\frac{220 a^3 \log (a+b x)}{b^{13}}+\frac{55 a^2 x}{b^{12}}-\frac{5 a x^2}{b^{11}}+\frac{x^3}{3 b^{10}} \]
Antiderivative was successfully verified.
[In] Int[x^12/(a + b*x)^10,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{12}}{9 b^{13} \left (a + b x\right )^{9}} + \frac{3 a^{11}}{2 b^{13} \left (a + b x\right )^{8}} - \frac{66 a^{10}}{7 b^{13} \left (a + b x\right )^{7}} + \frac{110 a^{9}}{3 b^{13} \left (a + b x\right )^{6}} - \frac{99 a^{8}}{b^{13} \left (a + b x\right )^{5}} + \frac{198 a^{7}}{b^{13} \left (a + b x\right )^{4}} - \frac{308 a^{6}}{b^{13} \left (a + b x\right )^{3}} + \frac{396 a^{5}}{b^{13} \left (a + b x\right )^{2}} - \frac{495 a^{4}}{b^{13} \left (a + b x\right )} - \frac{220 a^{3} \log{\left (a + b x \right )}}{b^{13}} + \frac{55 a^{2} x}{b^{12}} - \frac{10 a \int x\, dx}{b^{11}} + \frac{x^{3}}{3 b^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**12/(b*x+a)**10,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0845597, size = 161, normalized size = 0.87 \[ -\frac{35201 a^{12}+289089 a^{11} b x+1031616 a^{10} b^2 x^2+2074464 a^9 b^3 x^3+2529576 a^8 b^4 x^4+1831032 a^7 b^5 x^5+638568 a^6 b^6 x^6-58968 a^5 b^7 x^7-139482 a^4 b^8 x^8-43218 a^3 b^9 x^9+27720 a^3 (a+b x)^9 \log (a+b x)-2772 a^2 b^{10} x^{10}+252 a b^{11} x^{11}-42 b^{12} x^{12}}{126 b^{13} (a+b x)^9} \]
Antiderivative was successfully verified.
[In] Integrate[x^12/(a + b*x)^10,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.017, size = 177, normalized size = 1. \[ 55\,{\frac{{a}^{2}x}{{b}^{12}}}-5\,{\frac{a{x}^{2}}{{b}^{11}}}+{\frac{{x}^{3}}{3\,{b}^{10}}}-{\frac{{a}^{12}}{9\,{b}^{13} \left ( bx+a \right ) ^{9}}}+{\frac{3\,{a}^{11}}{2\,{b}^{13} \left ( bx+a \right ) ^{8}}}-{\frac{66\,{a}^{10}}{7\,{b}^{13} \left ( bx+a \right ) ^{7}}}+{\frac{110\,{a}^{9}}{3\,{b}^{13} \left ( bx+a \right ) ^{6}}}-99\,{\frac{{a}^{8}}{{b}^{13} \left ( bx+a \right ) ^{5}}}+198\,{\frac{{a}^{7}}{{b}^{13} \left ( bx+a \right ) ^{4}}}-308\,{\frac{{a}^{6}}{{b}^{13} \left ( bx+a \right ) ^{3}}}+396\,{\frac{{a}^{5}}{{b}^{13} \left ( bx+a \right ) ^{2}}}-495\,{\frac{{a}^{4}}{{b}^{13} \left ( bx+a \right ) }}-220\,{\frac{{a}^{3}\ln \left ( bx+a \right ) }{{b}^{13}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^12/(b*x+a)^10,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.37466, size = 316, normalized size = 1.7 \[ -\frac{62370 \, a^{4} b^{8} x^{8} + 449064 \, a^{5} b^{7} x^{7} + 1435896 \, a^{6} b^{6} x^{6} + 2652804 \, a^{7} b^{5} x^{5} + 3089394 \, a^{8} b^{4} x^{4} + 2318316 \, a^{9} b^{3} x^{3} + 1093356 \, a^{10} b^{2} x^{2} + 296019 \, a^{11} b x + 35201 \, a^{12}}{126 \,{\left (b^{22} x^{9} + 9 \, a b^{21} x^{8} + 36 \, a^{2} b^{20} x^{7} + 84 \, a^{3} b^{19} x^{6} + 126 \, a^{4} b^{18} x^{5} + 126 \, a^{5} b^{17} x^{4} + 84 \, a^{6} b^{16} x^{3} + 36 \, a^{7} b^{15} x^{2} + 9 \, a^{8} b^{14} x + a^{9} b^{13}\right )}} - \frac{220 \, a^{3} \log \left (b x + a\right )}{b^{13}} + \frac{b^{2} x^{3} - 15 \, a b x^{2} + 165 \, a^{2} x}{3 \, b^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^12/(b*x + a)^10,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.213775, size = 456, normalized size = 2.45 \[ \frac{42 \, b^{12} x^{12} - 252 \, a b^{11} x^{11} + 2772 \, a^{2} b^{10} x^{10} + 43218 \, a^{3} b^{9} x^{9} + 139482 \, a^{4} b^{8} x^{8} + 58968 \, a^{5} b^{7} x^{7} - 638568 \, a^{6} b^{6} x^{6} - 1831032 \, a^{7} b^{5} x^{5} - 2529576 \, a^{8} b^{4} x^{4} - 2074464 \, a^{9} b^{3} x^{3} - 1031616 \, a^{10} b^{2} x^{2} - 289089 \, a^{11} b x - 35201 \, a^{12} - 27720 \,{\left (a^{3} b^{9} x^{9} + 9 \, a^{4} b^{8} x^{8} + 36 \, a^{5} b^{7} x^{7} + 84 \, a^{6} b^{6} x^{6} + 126 \, a^{7} b^{5} x^{5} + 126 \, a^{8} b^{4} x^{4} + 84 \, a^{9} b^{3} x^{3} + 36 \, a^{10} b^{2} x^{2} + 9 \, a^{11} b x + a^{12}\right )} \log \left (b x + a\right )}{126 \,{\left (b^{22} x^{9} + 9 \, a b^{21} x^{8} + 36 \, a^{2} b^{20} x^{7} + 84 \, a^{3} b^{19} x^{6} + 126 \, a^{4} b^{18} x^{5} + 126 \, a^{5} b^{17} x^{4} + 84 \, a^{6} b^{16} x^{3} + 36 \, a^{7} b^{15} x^{2} + 9 \, a^{8} b^{14} x + a^{9} b^{13}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^12/(b*x + a)^10,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 5.90638, size = 248, normalized size = 1.33 \[ - \frac{220 a^{3} \log{\left (a + b x \right )}}{b^{13}} + \frac{55 a^{2} x}{b^{12}} - \frac{5 a x^{2}}{b^{11}} - \frac{35201 a^{12} + 296019 a^{11} b x + 1093356 a^{10} b^{2} x^{2} + 2318316 a^{9} b^{3} x^{3} + 3089394 a^{8} b^{4} x^{4} + 2652804 a^{7} b^{5} x^{5} + 1435896 a^{6} b^{6} x^{6} + 449064 a^{5} b^{7} x^{7} + 62370 a^{4} b^{8} x^{8}}{126 a^{9} b^{13} + 1134 a^{8} b^{14} x + 4536 a^{7} b^{15} x^{2} + 10584 a^{6} b^{16} x^{3} + 15876 a^{5} b^{17} x^{4} + 15876 a^{4} b^{18} x^{5} + 10584 a^{3} b^{19} x^{6} + 4536 a^{2} b^{20} x^{7} + 1134 a b^{21} x^{8} + 126 b^{22} x^{9}} + \frac{x^{3}}{3 b^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**12/(b*x+a)**10,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.234896, size = 201, normalized size = 1.08 \[ -\frac{220 \, a^{3}{\rm ln}\left ({\left | b x + a \right |}\right )}{b^{13}} - \frac{62370 \, a^{4} b^{8} x^{8} + 449064 \, a^{5} b^{7} x^{7} + 1435896 \, a^{6} b^{6} x^{6} + 2652804 \, a^{7} b^{5} x^{5} + 3089394 \, a^{8} b^{4} x^{4} + 2318316 \, a^{9} b^{3} x^{3} + 1093356 \, a^{10} b^{2} x^{2} + 296019 \, a^{11} b x + 35201 \, a^{12}}{126 \,{\left (b x + a\right )}^{9} b^{13}} + \frac{b^{20} x^{3} - 15 \, a b^{19} x^{2} + 165 \, a^{2} b^{18} x}{3 \, b^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^12/(b*x + a)^10,x, algorithm="giac")
[Out]