Optimal. Leaf size=82 \[ -\frac{a^6 c^5}{2 x^2}+\frac{4 a^5 b c^5}{x}+5 a^4 b^2 c^5 \log (x)-\frac{5}{2} a^2 b^4 c^5 x^2+\frac{4}{3} a b^5 c^5 x^3-\frac{1}{4} b^6 c^5 x^4 \]
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Rubi [A] time = 0.0996539, antiderivative size = 82, 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 \[ -\frac{a^6 c^5}{2 x^2}+\frac{4 a^5 b c^5}{x}+5 a^4 b^2 c^5 \log (x)-\frac{5}{2} a^2 b^4 c^5 x^2+\frac{4}{3} a b^5 c^5 x^3-\frac{1}{4} b^6 c^5 x^4 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^5)/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{6} c^{5}}{2 x^{2}} + \frac{4 a^{5} b c^{5}}{x} + 5 a^{4} b^{2} c^{5} \log{\left (x \right )} - 5 a^{2} b^{4} c^{5} \int x\, dx + \frac{4 a b^{5} c^{5} x^{3}}{3} - \frac{b^{6} c^{5} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**5/x**3,x)
[Out]
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Mathematica [A] time = 0.0116138, size = 68, normalized size = 0.83 \[ c^5 \left (-\frac{a^6}{2 x^2}+\frac{4 a^5 b}{x}+5 a^4 b^2 \log (x)-\frac{5}{2} a^2 b^4 x^2+\frac{4}{3} a b^5 x^3-\frac{b^6 x^4}{4}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^3,x]
[Out]
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Maple [A] time = 0.012, size = 75, normalized size = 0.9 \[ -{\frac{{a}^{6}{c}^{5}}{2\,{x}^{2}}}+4\,{\frac{{a}^{5}b{c}^{5}}{x}}-{\frac{5\,{a}^{2}{b}^{4}{c}^{5}{x}^{2}}{2}}+{\frac{4\,a{b}^{5}{c}^{5}{x}^{3}}{3}}-{\frac{{b}^{6}{c}^{5}{x}^{4}}{4}}+5\,{a}^{4}{b}^{2}{c}^{5}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^5/x^3,x)
[Out]
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Maxima [A] time = 1.43133, size = 101, normalized size = 1.23 \[ -\frac{1}{4} \, b^{6} c^{5} x^{4} + \frac{4}{3} \, a b^{5} c^{5} x^{3} - \frac{5}{2} \, a^{2} b^{4} c^{5} x^{2} + 5 \, a^{4} b^{2} c^{5} \log \left (x\right ) + \frac{8 \, a^{5} b c^{5} x - a^{6} c^{5}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205664, size = 104, normalized size = 1.27 \[ -\frac{3 \, b^{6} c^{5} x^{6} - 16 \, a b^{5} c^{5} x^{5} + 30 \, a^{2} b^{4} c^{5} x^{4} - 60 \, a^{4} b^{2} c^{5} x^{2} \log \left (x\right ) - 48 \, a^{5} b c^{5} x + 6 \, a^{6} c^{5}}{12 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.67691, size = 82, normalized size = 1. \[ 5 a^{4} b^{2} c^{5} \log{\left (x \right )} - \frac{5 a^{2} b^{4} c^{5} x^{2}}{2} + \frac{4 a b^{5} c^{5} x^{3}}{3} - \frac{b^{6} c^{5} x^{4}}{4} + \frac{- a^{6} c^{5} + 8 a^{5} b c^{5} x}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**5/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.239884, size = 103, normalized size = 1.26 \[ -\frac{1}{4} \, b^{6} c^{5} x^{4} + \frac{4}{3} \, a b^{5} c^{5} x^{3} - \frac{5}{2} \, a^{2} b^{4} c^{5} x^{2} + 5 \, a^{4} b^{2} c^{5}{\rm ln}\left ({\left | x \right |}\right ) + \frac{8 \, a^{5} b c^{5} x - a^{6} c^{5}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^3,x, algorithm="giac")
[Out]