Optimal. Leaf size=58 \[ -\frac{1458 x^7}{35}-\frac{7047 x^6}{50}-\frac{106677 x^5}{625}-\frac{152469 x^4}{2500}+\frac{152469 x^3}{3125}+\frac{1777779 x^2}{31250}+\frac{1666663 x}{78125}+\frac{11 \log (5 x+3)}{390625} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0505343, antiderivative size = 58, 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 \[ -\frac{1458 x^7}{35}-\frac{7047 x^6}{50}-\frac{106677 x^5}{625}-\frac{152469 x^4}{2500}+\frac{152469 x^3}{3125}+\frac{1777779 x^2}{31250}+\frac{1666663 x}{78125}+\frac{11 \log (5 x+3)}{390625} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{1458 x^{7}}{35} - \frac{7047 x^{6}}{50} - \frac{106677 x^{5}}{625} - \frac{152469 x^{4}}{2500} + \frac{152469 x^{3}}{3125} + \frac{11 \log{\left (5 x + 3 \right )}}{390625} + \int \frac{1666663}{78125}\, dx + \frac{1777779 \int x\, dx}{15625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)**6/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0253446, size = 47, normalized size = 0.81 \[ \frac{-2278125000 x^7-7707656250 x^6-9334237500 x^5-3335259375 x^4+2668207500 x^3+3111113250 x^2+1166664100 x+1540 \log (5 x+3)+158585307}{54687500} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 43, normalized size = 0.7 \[{\frac{1666663\,x}{78125}}+{\frac{1777779\,{x}^{2}}{31250}}+{\frac{152469\,{x}^{3}}{3125}}-{\frac{152469\,{x}^{4}}{2500}}-{\frac{106677\,{x}^{5}}{625}}-{\frac{7047\,{x}^{6}}{50}}-{\frac{1458\,{x}^{7}}{35}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{390625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)^6/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35307, size = 57, normalized size = 0.98 \[ -\frac{1458}{35} \, x^{7} - \frac{7047}{50} \, x^{6} - \frac{106677}{625} \, x^{5} - \frac{152469}{2500} \, x^{4} + \frac{152469}{3125} \, x^{3} + \frac{1777779}{31250} \, x^{2} + \frac{1666663}{78125} \, x + \frac{11}{390625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6*(2*x - 1)/(5*x + 3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.212154, size = 57, normalized size = 0.98 \[ -\frac{1458}{35} \, x^{7} - \frac{7047}{50} \, x^{6} - \frac{106677}{625} \, x^{5} - \frac{152469}{2500} \, x^{4} + \frac{152469}{3125} \, x^{3} + \frac{1777779}{31250} \, x^{2} + \frac{1666663}{78125} \, x + \frac{11}{390625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6*(2*x - 1)/(5*x + 3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.206142, size = 54, normalized size = 0.93 \[ - \frac{1458 x^{7}}{35} - \frac{7047 x^{6}}{50} - \frac{106677 x^{5}}{625} - \frac{152469 x^{4}}{2500} + \frac{152469 x^{3}}{3125} + \frac{1777779 x^{2}}{31250} + \frac{1666663 x}{78125} + \frac{11 \log{\left (5 x + 3 \right )}}{390625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)**6/(3+5*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.206683, size = 58, normalized size = 1. \[ -\frac{1458}{35} \, x^{7} - \frac{7047}{50} \, x^{6} - \frac{106677}{625} \, x^{5} - \frac{152469}{2500} \, x^{4} + \frac{152469}{3125} \, x^{3} + \frac{1777779}{31250} \, x^{2} + \frac{1666663}{78125} \, x + \frac{11}{390625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6*(2*x - 1)/(5*x + 3),x, algorithm="giac")
[Out]