Optimal. Leaf size=154 \[ \frac{a^9}{9 b^{10} (a+b x)^9}-\frac{9 a^8}{8 b^{10} (a+b x)^8}+\frac{36 a^7}{7 b^{10} (a+b x)^7}-\frac{14 a^6}{b^{10} (a+b x)^6}+\frac{126 a^5}{5 b^{10} (a+b x)^5}-\frac{63 a^4}{2 b^{10} (a+b x)^4}+\frac{28 a^3}{b^{10} (a+b x)^3}-\frac{18 a^2}{b^{10} (a+b x)^2}+\frac{9 a}{b^{10} (a+b x)}+\frac{\log (a+b x)}{b^{10}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.231525, antiderivative size = 154, 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 \[ \frac{a^9}{9 b^{10} (a+b x)^9}-\frac{9 a^8}{8 b^{10} (a+b x)^8}+\frac{36 a^7}{7 b^{10} (a+b x)^7}-\frac{14 a^6}{b^{10} (a+b x)^6}+\frac{126 a^5}{5 b^{10} (a+b x)^5}-\frac{63 a^4}{2 b^{10} (a+b x)^4}+\frac{28 a^3}{b^{10} (a+b x)^3}-\frac{18 a^2}{b^{10} (a+b x)^2}+\frac{9 a}{b^{10} (a+b x)}+\frac{\log (a+b x)}{b^{10}} \]
Antiderivative was successfully verified.
[In] Int[x^9/(a + b*x)^10,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 42.3444, size = 150, normalized size = 0.97 \[ \frac{a^{9}}{9 b^{10} \left (a + b x\right )^{9}} - \frac{9 a^{8}}{8 b^{10} \left (a + b x\right )^{8}} + \frac{36 a^{7}}{7 b^{10} \left (a + b x\right )^{7}} - \frac{14 a^{6}}{b^{10} \left (a + b x\right )^{6}} + \frac{126 a^{5}}{5 b^{10} \left (a + b x\right )^{5}} - \frac{63 a^{4}}{2 b^{10} \left (a + b x\right )^{4}} + \frac{28 a^{3}}{b^{10} \left (a + b x\right )^{3}} - \frac{18 a^{2}}{b^{10} \left (a + b x\right )^{2}} + \frac{9 a}{b^{10} \left (a + b x\right )} + \frac{\log{\left (a + b x \right )}}{b^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**9/(b*x+a)**10,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0506274, size = 111, normalized size = 0.72 \[ \frac{a \left (7129 a^8+61641 a^7 b x+235224 a^6 b^2 x^2+518616 a^5 b^3 x^3+725004 a^4 b^4 x^4+661500 a^3 b^5 x^5+388080 a^2 b^6 x^6+136080 a b^7 x^7+22680 b^8 x^8\right )}{2520 b^{10} (a+b x)^9}+\frac{\log (a+b x)}{b^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[x^9/(a + b*x)^10,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.011, size = 145, normalized size = 0.9 \[{\frac{{a}^{9}}{9\,{b}^{10} \left ( bx+a \right ) ^{9}}}-{\frac{9\,{a}^{8}}{8\,{b}^{10} \left ( bx+a \right ) ^{8}}}+{\frac{36\,{a}^{7}}{7\,{b}^{10} \left ( bx+a \right ) ^{7}}}-14\,{\frac{{a}^{6}}{{b}^{10} \left ( bx+a \right ) ^{6}}}+{\frac{126\,{a}^{5}}{5\,{b}^{10} \left ( bx+a \right ) ^{5}}}-{\frac{63\,{a}^{4}}{2\,{b}^{10} \left ( bx+a \right ) ^{4}}}+28\,{\frac{{a}^{3}}{{b}^{10} \left ( bx+a \right ) ^{3}}}-18\,{\frac{{a}^{2}}{{b}^{10} \left ( bx+a \right ) ^{2}}}+9\,{\frac{a}{{b}^{10} \left ( bx+a \right ) }}+{\frac{\ln \left ( bx+a \right ) }{{b}^{10}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^9/(b*x+a)^10,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34663, size = 273, normalized size = 1.77 \[ \frac{22680 \, a b^{8} x^{8} + 136080 \, a^{2} b^{7} x^{7} + 388080 \, a^{3} b^{6} x^{6} + 661500 \, a^{4} b^{5} x^{5} + 725004 \, a^{5} b^{4} x^{4} + 518616 \, a^{6} b^{3} x^{3} + 235224 \, a^{7} b^{2} x^{2} + 61641 \, a^{8} b x + 7129 \, a^{9}}{2520 \,{\left (b^{19} x^{9} + 9 \, a b^{18} x^{8} + 36 \, a^{2} b^{17} x^{7} + 84 \, a^{3} b^{16} x^{6} + 126 \, a^{4} b^{15} x^{5} + 126 \, a^{5} b^{14} x^{4} + 84 \, a^{6} b^{13} x^{3} + 36 \, a^{7} b^{12} x^{2} + 9 \, a^{8} b^{11} x + a^{9} b^{10}\right )}} + \frac{\log \left (b x + a\right )}{b^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x + a)^10,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.205123, size = 394, normalized size = 2.56 \[ \frac{22680 \, a b^{8} x^{8} + 136080 \, a^{2} b^{7} x^{7} + 388080 \, a^{3} b^{6} x^{6} + 661500 \, a^{4} b^{5} x^{5} + 725004 \, a^{5} b^{4} x^{4} + 518616 \, a^{6} b^{3} x^{3} + 235224 \, a^{7} b^{2} x^{2} + 61641 \, a^{8} b x + 7129 \, a^{9} + 2520 \,{\left (b^{9} x^{9} + 9 \, a b^{8} x^{8} + 36 \, a^{2} b^{7} x^{7} + 84 \, a^{3} b^{6} x^{6} + 126 \, a^{4} b^{5} x^{5} + 126 \, a^{5} b^{4} x^{4} + 84 \, a^{6} b^{3} x^{3} + 36 \, a^{7} b^{2} x^{2} + 9 \, a^{8} b x + a^{9}\right )} \log \left (b x + a\right )}{2520 \,{\left (b^{19} x^{9} + 9 \, a b^{18} x^{8} + 36 \, a^{2} b^{17} x^{7} + 84 \, a^{3} b^{16} x^{6} + 126 \, a^{4} b^{15} x^{5} + 126 \, a^{5} b^{14} x^{4} + 84 \, a^{6} b^{13} x^{3} + 36 \, a^{7} b^{12} x^{2} + 9 \, a^{8} b^{11} x + a^{9} b^{10}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x + a)^10,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.54877, size = 212, normalized size = 1.38 \[ \frac{7129 a^{9} + 61641 a^{8} b x + 235224 a^{7} b^{2} x^{2} + 518616 a^{6} b^{3} x^{3} + 725004 a^{5} b^{4} x^{4} + 661500 a^{4} b^{5} x^{5} + 388080 a^{3} b^{6} x^{6} + 136080 a^{2} b^{7} x^{7} + 22680 a b^{8} x^{8}}{2520 a^{9} b^{10} + 22680 a^{8} b^{11} x + 90720 a^{7} b^{12} x^{2} + 211680 a^{6} b^{13} x^{3} + 317520 a^{5} b^{14} x^{4} + 317520 a^{4} b^{15} x^{5} + 211680 a^{3} b^{16} x^{6} + 90720 a^{2} b^{17} x^{7} + 22680 a b^{18} x^{8} + 2520 b^{19} x^{9}} + \frac{\log{\left (a + b x \right )}}{b^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**9/(b*x+a)**10,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.213873, size = 151, normalized size = 0.98 \[ \frac{{\rm ln}\left ({\left | b x + a \right |}\right )}{b^{10}} + \frac{22680 \, a b^{7} x^{8} + 136080 \, a^{2} b^{6} x^{7} + 388080 \, a^{3} b^{5} x^{6} + 661500 \, a^{4} b^{4} x^{5} + 725004 \, a^{5} b^{3} x^{4} + 518616 \, a^{6} b^{2} x^{3} + 235224 \, a^{7} b x^{2} + 61641 \, a^{8} x + \frac{7129 \, a^{9}}{b}}{2520 \,{\left (b x + a\right )}^{9} b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x + a)^10,x, algorithm="giac")
[Out]