Optimal. Leaf size=75 \[ -\frac{a^6 c^5}{x}-4 a^5 b c^5 \log (x)+5 a^4 b^2 c^5 x-\frac{5}{3} a^2 b^4 c^5 x^3+a b^5 c^5 x^4-\frac{1}{5} b^6 c^5 x^5 \]
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Rubi [A] time = 0.0980214, 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 \[ -\frac{a^6 c^5}{x}-4 a^5 b c^5 \log (x)+5 a^4 b^2 c^5 x-\frac{5}{3} a^2 b^4 c^5 x^3+a b^5 c^5 x^4-\frac{1}{5} b^6 c^5 x^5 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^5)/x^2,x]
[Out]
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Rubi in Sympy [A] time = 28.5862, size = 75, normalized size = 1. \[ - \frac{a^{6} c^{5}}{x} - 4 a^{5} b c^{5} \log{\left (x \right )} + 5 a^{4} b^{2} c^{5} x - \frac{5 a^{2} b^{4} c^{5} x^{3}}{3} + a b^{5} c^{5} x^{4} - \frac{b^{6} c^{5} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**5/x**2,x)
[Out]
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Mathematica [A] time = 0.0114794, size = 61, normalized size = 0.81 \[ c^5 \left (-\frac{a^6}{x}-4 a^5 b \log (x)+5 a^4 b^2 x-\frac{5}{3} a^2 b^4 x^3+a b^5 x^4-\frac{b^6 x^5}{5}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^2,x]
[Out]
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Maple [A] time = 0.01, size = 72, normalized size = 1. \[ -{\frac{{a}^{6}{c}^{5}}{x}}+5\,{a}^{4}{b}^{2}{c}^{5}x-{\frac{5\,{a}^{2}{b}^{4}{c}^{5}{x}^{3}}{3}}+a{b}^{5}{c}^{5}{x}^{4}-{\frac{{b}^{6}{c}^{5}{x}^{5}}{5}}-4\,{a}^{5}b{c}^{5}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^5/x^2,x)
[Out]
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Maxima [A] time = 1.33863, size = 96, normalized size = 1.28 \[ -\frac{1}{5} \, b^{6} c^{5} x^{5} + a b^{5} c^{5} x^{4} - \frac{5}{3} \, a^{2} b^{4} c^{5} x^{3} + 5 \, a^{4} b^{2} c^{5} x - 4 \, a^{5} b c^{5} \log \left (x\right ) - \frac{a^{6} c^{5}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205273, size = 104, normalized size = 1.39 \[ -\frac{3 \, b^{6} c^{5} x^{6} - 15 \, a b^{5} c^{5} x^{5} + 25 \, a^{2} b^{4} c^{5} x^{4} - 75 \, a^{4} b^{2} c^{5} x^{2} + 60 \, a^{5} b c^{5} x \log \left (x\right ) + 15 \, a^{6} c^{5}}{15 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.42978, size = 75, normalized size = 1. \[ - \frac{a^{6} c^{5}}{x} - 4 a^{5} b c^{5} \log{\left (x \right )} + 5 a^{4} b^{2} c^{5} x - \frac{5 a^{2} b^{4} c^{5} x^{3}}{3} + a b^{5} c^{5} x^{4} - \frac{b^{6} c^{5} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**5/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.320218, size = 97, normalized size = 1.29 \[ -\frac{1}{5} \, b^{6} c^{5} x^{5} + a b^{5} c^{5} x^{4} - \frac{5}{3} \, a^{2} b^{4} c^{5} x^{3} + 5 \, a^{4} b^{2} c^{5} x - 4 \, a^{5} b c^{5}{\rm ln}\left ({\left | x \right |}\right ) - \frac{a^{6} c^{5}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^2,x, algorithm="giac")
[Out]