Optimal. Leaf size=79 \[ a^6 c^5 \log (x)-4 a^5 b c^5 x+\frac{5}{2} a^4 b^2 c^5 x^2-\frac{5}{4} a^2 b^4 c^5 x^4+\frac{4}{5} a b^5 c^5 x^5-\frac{1}{6} b^6 c^5 x^6 \]
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Rubi [A] time = 0.0785363, antiderivative size = 79, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ a^6 c^5 \log (x)-4 a^5 b c^5 x+\frac{5}{2} a^4 b^2 c^5 x^2-\frac{5}{4} a^2 b^4 c^5 x^4+\frac{4}{5} a b^5 c^5 x^5-\frac{1}{6} b^6 c^5 x^6 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^5)/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{6} c^{5} \log{\left (x \right )} - 4 a^{5} b c^{5} x + 5 a^{4} b^{2} c^{5} \int x\, dx - \frac{5 a^{2} b^{4} c^{5} x^{4}}{4} + \frac{4 a b^{5} c^{5} x^{5}}{5} - \frac{b^{6} c^{5} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**5/x,x)
[Out]
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Mathematica [A] time = 0.0205116, size = 75, normalized size = 0.95 \[ c^5 \left (a^6 \log (-b x)+\frac{127 a^6}{60}-4 a^5 b x+\frac{5}{2} a^4 b^2 x^2-\frac{5}{4} a^2 b^4 x^4+\frac{4}{5} a b^5 x^5-\frac{b^6 x^6}{6}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^5)/x,x]
[Out]
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Maple [A] time = 0.004, size = 72, normalized size = 0.9 \[ -4\,{a}^{5}b{c}^{5}x+{\frac{5\,{a}^{4}{b}^{2}{c}^{5}{x}^{2}}{2}}-{\frac{5\,{a}^{2}{b}^{4}{c}^{5}{x}^{4}}{4}}+{\frac{4\,a{b}^{5}{c}^{5}{x}^{5}}{5}}-{\frac{{b}^{6}{c}^{5}{x}^{6}}{6}}+{a}^{6}{c}^{5}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^5/x,x)
[Out]
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Maxima [A] time = 1.3819, size = 96, normalized size = 1.22 \[ -\frac{1}{6} \, b^{6} c^{5} x^{6} + \frac{4}{5} \, a b^{5} c^{5} x^{5} - \frac{5}{4} \, a^{2} b^{4} c^{5} x^{4} + \frac{5}{2} \, a^{4} b^{2} c^{5} x^{2} - 4 \, a^{5} b c^{5} x + a^{6} c^{5} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205614, size = 96, normalized size = 1.22 \[ -\frac{1}{6} \, b^{6} c^{5} x^{6} + \frac{4}{5} \, a b^{5} c^{5} x^{5} - \frac{5}{4} \, a^{2} b^{4} c^{5} x^{4} + \frac{5}{2} \, a^{4} b^{2} c^{5} x^{2} - 4 \, a^{5} b c^{5} x + a^{6} c^{5} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.31218, size = 82, normalized size = 1.04 \[ a^{6} c^{5} \log{\left (x \right )} - 4 a^{5} b c^{5} x + \frac{5 a^{4} b^{2} c^{5} x^{2}}{2} - \frac{5 a^{2} b^{4} c^{5} x^{4}}{4} + \frac{4 a b^{5} c^{5} x^{5}}{5} - \frac{b^{6} c^{5} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**5/x,x)
[Out]
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GIAC/XCAS [A] time = 0.247664, size = 97, normalized size = 1.23 \[ -\frac{1}{6} \, b^{6} c^{5} x^{6} + \frac{4}{5} \, a b^{5} c^{5} x^{5} - \frac{5}{4} \, a^{2} b^{4} c^{5} x^{4} + \frac{5}{2} \, a^{4} b^{2} c^{5} x^{2} - 4 \, a^{5} b c^{5} x + a^{6} c^{5}{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x,x, algorithm="giac")
[Out]