Optimal. Leaf size=99 \[ \frac{b^7}{2 a^8 (a x+b)^2}-\frac{7 b^6}{a^8 (a x+b)}-\frac{21 b^5 \log (a x+b)}{a^8}+\frac{15 b^4 x}{a^7}-\frac{5 b^3 x^2}{a^6}+\frac{2 b^2 x^3}{a^5}-\frac{3 b x^4}{4 a^4}+\frac{x^5}{5 a^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.171119, antiderivative size = 99, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{b^7}{2 a^8 (a x+b)^2}-\frac{7 b^6}{a^8 (a x+b)}-\frac{21 b^5 \log (a x+b)}{a^8}+\frac{15 b^4 x}{a^7}-\frac{5 b^3 x^2}{a^6}+\frac{2 b^2 x^3}{a^5}-\frac{3 b x^4}{4 a^4}+\frac{x^5}{5 a^3} \]
Antiderivative was successfully verified.
[In] Int[x^4/(a + b/x)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{5}}{5 a^{3}} - \frac{3 b x^{4}}{4 a^{4}} + \frac{2 b^{2} x^{3}}{a^{5}} - \frac{10 b^{3} \int x\, dx}{a^{6}} + \frac{15 b^{4} x}{a^{7}} + \frac{b^{7}}{2 a^{8} \left (a x + b\right )^{2}} - \frac{7 b^{6}}{a^{8} \left (a x + b\right )} - \frac{21 b^{5} \log{\left (a x + b \right )}}{a^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(a+b/x)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0953809, size = 85, normalized size = 0.86 \[ \frac{4 a^5 x^5-15 a^4 b x^4+40 a^3 b^2 x^3-100 a^2 b^3 x^2-\frac{10 b^6 (14 a x+13 b)}{(a x+b)^2}-420 b^5 \log (a x+b)+300 a b^4 x}{20 a^8} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(a + b/x)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.012, size = 94, normalized size = 1. \[ 15\,{\frac{{b}^{4}x}{{a}^{7}}}-5\,{\frac{{b}^{3}{x}^{2}}{{a}^{6}}}+2\,{\frac{{b}^{2}{x}^{3}}{{a}^{5}}}-{\frac{3\,b{x}^{4}}{4\,{a}^{4}}}+{\frac{{x}^{5}}{5\,{a}^{3}}}+{\frac{{b}^{7}}{2\,{a}^{8} \left ( ax+b \right ) ^{2}}}-7\,{\frac{{b}^{6}}{{a}^{8} \left ( ax+b \right ) }}-21\,{\frac{{b}^{5}\ln \left ( ax+b \right ) }{{a}^{8}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(a+b/x)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43136, size = 139, normalized size = 1.4 \[ -\frac{14 \, a b^{6} x + 13 \, b^{7}}{2 \,{\left (a^{10} x^{2} + 2 \, a^{9} b x + a^{8} b^{2}\right )}} - \frac{21 \, b^{5} \log \left (a x + b\right )}{a^{8}} + \frac{4 \, a^{4} x^{5} - 15 \, a^{3} b x^{4} + 40 \, a^{2} b^{2} x^{3} - 100 \, a b^{3} x^{2} + 300 \, b^{4} x}{20 \, a^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(a + b/x)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.219393, size = 174, normalized size = 1.76 \[ \frac{4 \, a^{7} x^{7} - 7 \, a^{6} b x^{6} + 14 \, a^{5} b^{2} x^{5} - 35 \, a^{4} b^{3} x^{4} + 140 \, a^{3} b^{4} x^{3} + 500 \, a^{2} b^{5} x^{2} + 160 \, a b^{6} x - 130 \, b^{7} - 420 \,{\left (a^{2} b^{5} x^{2} + 2 \, a b^{6} x + b^{7}\right )} \log \left (a x + b\right )}{20 \,{\left (a^{10} x^{2} + 2 \, a^{9} b x + a^{8} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(a + b/x)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.89033, size = 107, normalized size = 1.08 \[ - \frac{14 a b^{6} x + 13 b^{7}}{2 a^{10} x^{2} + 4 a^{9} b x + 2 a^{8} b^{2}} + \frac{x^{5}}{5 a^{3}} - \frac{3 b x^{4}}{4 a^{4}} + \frac{2 b^{2} x^{3}}{a^{5}} - \frac{5 b^{3} x^{2}}{a^{6}} + \frac{15 b^{4} x}{a^{7}} - \frac{21 b^{5} \log{\left (a x + b \right )}}{a^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(a+b/x)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.223323, size = 128, normalized size = 1.29 \[ -\frac{21 \, b^{5}{\rm ln}\left ({\left | a x + b \right |}\right )}{a^{8}} - \frac{14 \, a b^{6} x + 13 \, b^{7}}{2 \,{\left (a x + b\right )}^{2} a^{8}} + \frac{4 \, a^{12} x^{5} - 15 \, a^{11} b x^{4} + 40 \, a^{10} b^{2} x^{3} - 100 \, a^{9} b^{3} x^{2} + 300 \, a^{8} b^{4} x}{20 \, a^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(a + b/x)^3,x, algorithm="giac")
[Out]