Optimal. Leaf size=72 \[ -\frac{a^5 c^4}{4 x^4}+\frac{a^4 b c^4}{x^3}-\frac{a^3 b^2 c^4}{x^2}-\frac{2 a^2 b^3 c^4}{x}-3 a b^4 c^4 \log (x)+b^5 c^4 x \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0953821, antiderivative size = 72, 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 \[ -\frac{a^5 c^4}{4 x^4}+\frac{a^4 b c^4}{x^3}-\frac{a^3 b^2 c^4}{x^2}-\frac{2 a^2 b^3 c^4}{x}-3 a b^4 c^4 \log (x)+b^5 c^4 x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^4)/x^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{5} c^{4}}{4 x^{4}} + \frac{a^{4} b c^{4}}{x^{3}} - \frac{a^{3} b^{2} c^{4}}{x^{2}} - \frac{2 a^{2} b^{3} c^{4}}{x} - 3 a b^{4} c^{4} \log{\left (x \right )} + c^{4} \int b^{5}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**4/x**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0129897, size = 72, normalized size = 1. \[ -\frac{a^5 c^4}{4 x^4}+\frac{a^4 b c^4}{x^3}-\frac{a^3 b^2 c^4}{x^2}-\frac{2 a^2 b^3 c^4}{x}-3 a b^4 c^4 \log (x)+b^5 c^4 x \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^4)/x^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 71, normalized size = 1. \[ -{\frac{{a}^{5}{c}^{4}}{4\,{x}^{4}}}+{\frac{{a}^{4}b{c}^{4}}{{x}^{3}}}-{\frac{{a}^{3}{b}^{2}{c}^{4}}{{x}^{2}}}-2\,{\frac{{a}^{2}{b}^{3}{c}^{4}}{x}}+{b}^{5}{c}^{4}x-3\,a{b}^{4}{c}^{4}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^4/x^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.36321, size = 96, normalized size = 1.33 \[ b^{5} c^{4} x - 3 \, a b^{4} c^{4} \log \left (x\right ) - \frac{8 \, a^{2} b^{3} c^{4} x^{3} + 4 \, a^{3} b^{2} c^{4} x^{2} - 4 \, a^{4} b c^{4} x + a^{5} c^{4}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^4*(b*x + a)/x^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.211525, size = 104, normalized size = 1.44 \[ \frac{4 \, b^{5} c^{4} x^{5} - 12 \, a b^{4} c^{4} x^{4} \log \left (x\right ) - 8 \, a^{2} b^{3} c^{4} x^{3} - 4 \, a^{3} b^{2} c^{4} x^{2} + 4 \, a^{4} b c^{4} x - a^{5} c^{4}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^4*(b*x + a)/x^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.988506, size = 75, normalized size = 1.04 \[ - 3 a b^{4} c^{4} \log{\left (x \right )} + b^{5} c^{4} x - \frac{a^{5} c^{4} - 4 a^{4} b c^{4} x + 4 a^{3} b^{2} c^{4} x^{2} + 8 a^{2} b^{3} c^{4} x^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**4/x**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.274291, size = 97, normalized size = 1.35 \[ b^{5} c^{4} x - 3 \, a b^{4} c^{4}{\rm ln}\left ({\left | x \right |}\right ) - \frac{8 \, a^{2} b^{3} c^{4} x^{3} + 4 \, a^{3} b^{2} c^{4} x^{2} - 4 \, a^{4} b c^{4} x + a^{5} c^{4}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^4*(b*x + a)/x^5,x, algorithm="giac")
[Out]