Optimal. Leaf size=139 \[ \frac{a^9}{6 b^{10} (a+b x)^6}-\frac{9 a^8}{5 b^{10} (a+b x)^5}+\frac{9 a^7}{b^{10} (a+b x)^4}-\frac{28 a^6}{b^{10} (a+b x)^3}+\frac{63 a^5}{b^{10} (a+b x)^2}-\frac{126 a^4}{b^{10} (a+b x)}-\frac{84 a^3 \log (a+b x)}{b^{10}}+\frac{28 a^2 x}{b^9}-\frac{7 a x^2}{2 b^8}+\frac{x^3}{3 b^7} \]
[Out]
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Rubi [A] time = 0.236787, antiderivative size = 139, 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 \[ \frac{a^9}{6 b^{10} (a+b x)^6}-\frac{9 a^8}{5 b^{10} (a+b x)^5}+\frac{9 a^7}{b^{10} (a+b x)^4}-\frac{28 a^6}{b^{10} (a+b x)^3}+\frac{63 a^5}{b^{10} (a+b x)^2}-\frac{126 a^4}{b^{10} (a+b x)}-\frac{84 a^3 \log (a+b x)}{b^{10}}+\frac{28 a^2 x}{b^9}-\frac{7 a x^2}{2 b^8}+\frac{x^3}{3 b^7} \]
Antiderivative was successfully verified.
[In] Int[x^9/(a + b*x)^7,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{9}}{6 b^{10} \left (a + b x\right )^{6}} - \frac{9 a^{8}}{5 b^{10} \left (a + b x\right )^{5}} + \frac{9 a^{7}}{b^{10} \left (a + b x\right )^{4}} - \frac{28 a^{6}}{b^{10} \left (a + b x\right )^{3}} + \frac{63 a^{5}}{b^{10} \left (a + b x\right )^{2}} - \frac{126 a^{4}}{b^{10} \left (a + b x\right )} - \frac{84 a^{3} \log{\left (a + b x \right )}}{b^{10}} + \frac{28 a^{2} x}{b^{9}} - \frac{7 a \int x\, dx}{b^{8}} + \frac{x^{3}}{3 b^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**9/(b*x+a)**7,x)
[Out]
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Mathematica [A] time = 0.0566402, size = 128, normalized size = 0.92 \[ -\frac{2509 a^9+12534 a^8 b x+23775 a^7 b^2 x^2+19100 a^6 b^3 x^3+1725 a^5 b^4 x^4-6870 a^4 b^5 x^5-3665 a^3 b^6 x^6+2520 a^3 (a+b x)^6 \log (a+b x)-360 a^2 b^7 x^7+45 a b^8 x^8-10 b^9 x^9}{30 b^{10} (a+b x)^6} \]
Antiderivative was successfully verified.
[In] Integrate[x^9/(a + b*x)^7,x]
[Out]
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Maple [A] time = 0.015, size = 132, normalized size = 1. \[ 28\,{\frac{{a}^{2}x}{{b}^{9}}}-{\frac{7\,a{x}^{2}}{2\,{b}^{8}}}+{\frac{{x}^{3}}{3\,{b}^{7}}}+{\frac{{a}^{9}}{6\,{b}^{10} \left ( bx+a \right ) ^{6}}}-{\frac{9\,{a}^{8}}{5\,{b}^{10} \left ( bx+a \right ) ^{5}}}+9\,{\frac{{a}^{7}}{{b}^{10} \left ( bx+a \right ) ^{4}}}-28\,{\frac{{a}^{6}}{{b}^{10} \left ( bx+a \right ) ^{3}}}+63\,{\frac{{a}^{5}}{{b}^{10} \left ( bx+a \right ) ^{2}}}-126\,{\frac{{a}^{4}}{{b}^{10} \left ( bx+a \right ) }}-84\,{\frac{{a}^{3}\ln \left ( bx+a \right ) }{{b}^{10}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^9/(b*x+a)^7,x)
[Out]
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Maxima [A] time = 1.35391, size = 228, normalized size = 1.64 \[ -\frac{3780 \, a^{4} b^{5} x^{5} + 17010 \, a^{5} b^{4} x^{4} + 31080 \, a^{6} b^{3} x^{3} + 28710 \, a^{7} b^{2} x^{2} + 13374 \, a^{8} b x + 2509 \, a^{9}}{30 \,{\left (b^{16} x^{6} + 6 \, a b^{15} x^{5} + 15 \, a^{2} b^{14} x^{4} + 20 \, a^{3} b^{13} x^{3} + 15 \, a^{4} b^{12} x^{2} + 6 \, a^{5} b^{11} x + a^{6} b^{10}\right )}} - \frac{84 \, a^{3} \log \left (b x + a\right )}{b^{10}} + \frac{2 \, b^{2} x^{3} - 21 \, a b x^{2} + 168 \, a^{2} x}{6 \, b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x + a)^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208136, size = 323, normalized size = 2.32 \[ \frac{10 \, b^{9} x^{9} - 45 \, a b^{8} x^{8} + 360 \, a^{2} b^{7} x^{7} + 3665 \, a^{3} b^{6} x^{6} + 6870 \, a^{4} b^{5} x^{5} - 1725 \, a^{5} b^{4} x^{4} - 19100 \, a^{6} b^{3} x^{3} - 23775 \, a^{7} b^{2} x^{2} - 12534 \, a^{8} b x - 2509 \, a^{9} - 2520 \,{\left (a^{3} b^{6} x^{6} + 6 \, a^{4} b^{5} x^{5} + 15 \, a^{5} b^{4} x^{4} + 20 \, a^{6} b^{3} x^{3} + 15 \, a^{7} b^{2} x^{2} + 6 \, a^{8} b x + a^{9}\right )} \log \left (b x + a\right )}{30 \,{\left (b^{16} x^{6} + 6 \, a b^{15} x^{5} + 15 \, a^{2} b^{14} x^{4} + 20 \, a^{3} b^{13} x^{3} + 15 \, a^{4} b^{12} x^{2} + 6 \, a^{5} b^{11} x + a^{6} b^{10}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x + a)^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.73075, size = 178, normalized size = 1.28 \[ - \frac{84 a^{3} \log{\left (a + b x \right )}}{b^{10}} + \frac{28 a^{2} x}{b^{9}} - \frac{7 a x^{2}}{2 b^{8}} - \frac{2509 a^{9} + 13374 a^{8} b x + 28710 a^{7} b^{2} x^{2} + 31080 a^{6} b^{3} x^{3} + 17010 a^{5} b^{4} x^{4} + 3780 a^{4} b^{5} x^{5}}{30 a^{6} b^{10} + 180 a^{5} b^{11} x + 450 a^{4} b^{12} x^{2} + 600 a^{3} b^{13} x^{3} + 450 a^{2} b^{14} x^{4} + 180 a b^{15} x^{5} + 30 b^{16} x^{6}} + \frac{x^{3}}{3 b^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**9/(b*x+a)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.202908, size = 158, normalized size = 1.14 \[ -\frac{84 \, a^{3}{\rm ln}\left ({\left | b x + a \right |}\right )}{b^{10}} - \frac{3780 \, a^{4} b^{5} x^{5} + 17010 \, a^{5} b^{4} x^{4} + 31080 \, a^{6} b^{3} x^{3} + 28710 \, a^{7} b^{2} x^{2} + 13374 \, a^{8} b x + 2509 \, a^{9}}{30 \,{\left (b x + a\right )}^{6} b^{10}} + \frac{2 \, b^{14} x^{3} - 21 \, a b^{13} x^{2} + 168 \, a^{2} b^{12} x}{6 \, b^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x + a)^7,x, algorithm="giac")
[Out]