Optimal. Leaf size=75 \[ -\frac{a^6 c^5}{5 x^5}+\frac{a^5 b c^5}{x^4}-\frac{5 a^4 b^2 c^5}{3 x^3}+\frac{5 a^2 b^4 c^5}{x}+4 a b^5 c^5 \log (x)-b^6 c^5 x \]
[Out]
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Rubi [A] time = 0.0996664, antiderivative size = 75, 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 \[ -\frac{a^6 c^5}{5 x^5}+\frac{a^5 b c^5}{x^4}-\frac{5 a^4 b^2 c^5}{3 x^3}+\frac{5 a^2 b^4 c^5}{x}+4 a b^5 c^5 \log (x)-b^6 c^5 x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^5)/x^6,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{6} c^{5}}{5 x^{5}} + \frac{a^{5} b c^{5}}{x^{4}} - \frac{5 a^{4} b^{2} c^{5}}{3 x^{3}} + \frac{5 a^{2} b^{4} c^{5}}{x} + 4 a b^{5} c^{5} \log{\left (x \right )} - c^{5} \int b^{6}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**5/x**6,x)
[Out]
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Mathematica [A] time = 0.011138, size = 61, normalized size = 0.81 \[ c^5 \left (-\frac{a^6}{5 x^5}+\frac{a^5 b}{x^4}-\frac{5 a^4 b^2}{3 x^3}+\frac{5 a^2 b^4}{x}+4 a b^5 \log (x)-b^6 x\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^6,x]
[Out]
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Maple [A] time = 0.01, size = 72, normalized size = 1. \[ -{\frac{{a}^{6}{c}^{5}}{5\,{x}^{5}}}+{\frac{{a}^{5}b{c}^{5}}{{x}^{4}}}-{\frac{5\,{a}^{4}{b}^{2}{c}^{5}}{3\,{x}^{3}}}+5\,{\frac{{a}^{2}{b}^{4}{c}^{5}}{x}}-{b}^{6}{c}^{5}x+4\,a{b}^{5}{c}^{5}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^5/x^6,x)
[Out]
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Maxima [A] time = 1.33767, size = 99, normalized size = 1.32 \[ -b^{6} c^{5} x + 4 \, a b^{5} c^{5} \log \left (x\right ) + \frac{75 \, a^{2} b^{4} c^{5} x^{4} - 25 \, a^{4} b^{2} c^{5} x^{2} + 15 \, a^{5} b c^{5} x - 3 \, a^{6} c^{5}}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208575, size = 104, normalized size = 1.39 \[ -\frac{15 \, b^{6} c^{5} x^{6} - 60 \, a b^{5} c^{5} x^{5} \log \left (x\right ) - 75 \, a^{2} b^{4} c^{5} x^{4} + 25 \, a^{4} b^{2} c^{5} x^{2} - 15 \, a^{5} b c^{5} x + 3 \, a^{6} c^{5}}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.19792, size = 76, normalized size = 1.01 \[ 4 a b^{5} c^{5} \log{\left (x \right )} - b^{6} c^{5} x + \frac{- 3 a^{6} c^{5} + 15 a^{5} b c^{5} x - 25 a^{4} b^{2} c^{5} x^{2} + 75 a^{2} b^{4} c^{5} x^{4}}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**5/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.244273, size = 100, normalized size = 1.33 \[ -b^{6} c^{5} x + 4 \, a b^{5} c^{5}{\rm ln}\left ({\left | x \right |}\right ) + \frac{75 \, a^{2} b^{4} c^{5} x^{4} - 25 \, a^{4} b^{2} c^{5} x^{2} + 15 \, a^{5} b c^{5} x - 3 \, a^{6} c^{5}}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^6,x, algorithm="giac")
[Out]