Optimal. Leaf size=72 \[ \frac{a^5}{b^6 (a+b x)}+\frac{5 a^4 \log (a+b x)}{b^6}-\frac{4 a^3 x}{b^5}+\frac{3 a^2 x^2}{2 b^4}-\frac{2 a x^3}{3 b^3}+\frac{x^4}{4 b^2} \]
[Out]
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Rubi [A] time = 0.0895364, antiderivative size = 72, 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 \[ \frac{a^5}{b^6 (a+b x)}+\frac{5 a^4 \log (a+b x)}{b^6}-\frac{4 a^3 x}{b^5}+\frac{3 a^2 x^2}{2 b^4}-\frac{2 a x^3}{3 b^3}+\frac{x^4}{4 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^5/(a + b*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{5}}{b^{6} \left (a + b x\right )} + \frac{5 a^{4} \log{\left (a + b x \right )}}{b^{6}} - \frac{4 a^{3} x}{b^{5}} + \frac{3 a^{2} \int x\, dx}{b^{4}} - \frac{2 a x^{3}}{3 b^{3}} + \frac{x^{4}}{4 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.0277246, size = 66, normalized size = 0.92 \[ \frac{\frac{12 a^5}{a+b x}+60 a^4 \log (a+b x)-48 a^3 b x+18 a^2 b^2 x^2-8 a b^3 x^3+3 b^4 x^4}{12 b^6} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.012, size = 67, normalized size = 0.9 \[ -4\,{\frac{{a}^{3}x}{{b}^{5}}}+{\frac{3\,{a}^{2}{x}^{2}}{2\,{b}^{4}}}-{\frac{2\,a{x}^{3}}{3\,{b}^{3}}}+{\frac{{x}^{4}}{4\,{b}^{2}}}+{\frac{{a}^{5}}{{b}^{6} \left ( bx+a \right ) }}+5\,{\frac{{a}^{4}\ln \left ( bx+a \right ) }{{b}^{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.37676, size = 95, normalized size = 1.32 \[ \frac{a^{5}}{b^{7} x + a b^{6}} + \frac{5 \, a^{4} \log \left (b x + a\right )}{b^{6}} + \frac{3 \, b^{3} x^{4} - 8 \, a b^{2} x^{3} + 18 \, a^{2} b x^{2} - 48 \, a^{3} x}{12 \, b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.191743, size = 115, normalized size = 1.6 \[ \frac{3 \, b^{5} x^{5} - 5 \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x^{3} - 30 \, a^{3} b^{2} x^{2} - 48 \, a^{4} b x + 12 \, a^{5} + 60 \,{\left (a^{4} b x + a^{5}\right )} \log \left (b x + a\right )}{12 \,{\left (b^{7} x + a b^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.46896, size = 71, normalized size = 0.99 \[ \frac{a^{5}}{a b^{6} + b^{7} x} + \frac{5 a^{4} \log{\left (a + b x \right )}}{b^{6}} - \frac{4 a^{3} x}{b^{5}} + \frac{3 a^{2} x^{2}}{2 b^{4}} - \frac{2 a x^{3}}{3 b^{3}} + \frac{x^{4}}{4 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.216018, size = 122, normalized size = 1.69 \[ -\frac{{\left (b x + a\right )}^{4}{\left (\frac{20 \, a}{b x + a} - \frac{60 \, a^{2}}{{\left (b x + a\right )}^{2}} + \frac{120 \, a^{3}}{{\left (b x + a\right )}^{3}} - 3\right )}}{12 \, b^{6}} - \frac{5 \, a^{4}{\rm ln}\left (\frac{{\left | b x + a \right |}}{{\left (b x + a\right )}^{2}{\left | b \right |}}\right )}{b^{6}} + \frac{a^{5}}{{\left (b x + a\right )} b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x + a)^2,x, algorithm="giac")
[Out]