Optimal. Leaf size=81 \[ -\frac{a^6}{b^7 (a+b x)}-\frac{6 a^5 \log (a+b x)}{b^7}+\frac{5 a^4 x}{b^6}-\frac{2 a^3 x^2}{b^5}+\frac{a^2 x^3}{b^4}-\frac{a x^4}{2 b^3}+\frac{x^5}{5 b^2} \]
[Out]
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Rubi [A] time = 0.111031, antiderivative size = 81, 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 \[ -\frac{a^6}{b^7 (a+b x)}-\frac{6 a^5 \log (a+b x)}{b^7}+\frac{5 a^4 x}{b^6}-\frac{2 a^3 x^2}{b^5}+\frac{a^2 x^3}{b^4}-\frac{a x^4}{2 b^3}+\frac{x^5}{5 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^6/(a + b*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{6}}{b^{7} \left (a + b x\right )} - \frac{6 a^{5} \log{\left (a + b x \right )}}{b^{7}} + \frac{5 a^{4} x}{b^{6}} - \frac{4 a^{3} \int x\, dx}{b^{5}} + \frac{a^{2} x^{3}}{b^{4}} - \frac{a x^{4}}{2 b^{3}} + \frac{x^{5}}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**6/(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.0442018, size = 77, normalized size = 0.95 \[ \frac{-\frac{10 a^6}{a+b x}-60 a^5 \log (a+b x)+50 a^4 b x-20 a^3 b^2 x^2+10 a^2 b^3 x^3-5 a b^4 x^4+2 b^5 x^5}{10 b^7} \]
Antiderivative was successfully verified.
[In] Integrate[x^6/(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.01, size = 78, normalized size = 1. \[ 5\,{\frac{{a}^{4}x}{{b}^{6}}}-2\,{\frac{{a}^{3}{x}^{2}}{{b}^{5}}}+{\frac{{a}^{2}{x}^{3}}{{b}^{4}}}-{\frac{a{x}^{4}}{2\,{b}^{3}}}+{\frac{{x}^{5}}{5\,{b}^{2}}}-{\frac{{a}^{6}}{{b}^{7} \left ( bx+a \right ) }}-6\,{\frac{{a}^{5}\ln \left ( bx+a \right ) }{{b}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^6/(b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.3606, size = 111, normalized size = 1.37 \[ -\frac{a^{6}}{b^{8} x + a b^{7}} - \frac{6 \, a^{5} \log \left (b x + a\right )}{b^{7}} + \frac{2 \, b^{4} x^{5} - 5 \, a b^{3} x^{4} + 10 \, a^{2} b^{2} x^{3} - 20 \, a^{3} b x^{2} + 50 \, a^{4} x}{10 \, b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^6/(b*x + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.194298, size = 130, normalized size = 1.6 \[ \frac{2 \, b^{6} x^{6} - 3 \, a b^{5} x^{5} + 5 \, a^{2} b^{4} x^{4} - 10 \, a^{3} b^{3} x^{3} + 30 \, a^{4} b^{2} x^{2} + 50 \, a^{5} b x - 10 \, a^{6} - 60 \,{\left (a^{5} b x + a^{6}\right )} \log \left (b x + a\right )}{10 \,{\left (b^{8} x + a b^{7}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^6/(b*x + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.51226, size = 78, normalized size = 0.96 \[ - \frac{a^{6}}{a b^{7} + b^{8} x} - \frac{6 a^{5} \log{\left (a + b x \right )}}{b^{7}} + \frac{5 a^{4} x}{b^{6}} - \frac{2 a^{3} x^{2}}{b^{5}} + \frac{a^{2} x^{3}}{b^{4}} - \frac{a x^{4}}{2 b^{3}} + \frac{x^{5}}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**6/(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217648, size = 139, normalized size = 1.72 \[ -\frac{{\left (b x + a\right )}^{5}{\left (\frac{15 \, a}{b x + a} - \frac{50 \, a^{2}}{{\left (b x + a\right )}^{2}} + \frac{100 \, a^{3}}{{\left (b x + a\right )}^{3}} - \frac{150 \, a^{4}}{{\left (b x + a\right )}^{4}} - 2\right )}}{10 \, b^{7}} + \frac{6 \, a^{5}{\rm ln}\left (\frac{{\left | b x + a \right |}}{{\left (b x + a\right )}^{2}{\left | b \right |}}\right )}{b^{7}} - \frac{a^{6}}{{\left (b x + a\right )} b^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^6/(b*x + a)^2,x, algorithm="giac")
[Out]