Optimal. Leaf size=69 \[ -\frac{1944 x^7}{175}-\frac{1026 x^6}{125}+\frac{44982 x^5}{3125}+\frac{108387 x^4}{12500}-\frac{26594 x^3}{3125}-\frac{507023 x^2}{156250}+\frac{1382328 x}{390625}-\frac{1331}{1953125 (5 x+3)}+\frac{19239 \log (5 x+3)}{1953125} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0819064, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{1944 x^7}{175}-\frac{1026 x^6}{125}+\frac{44982 x^5}{3125}+\frac{108387 x^4}{12500}-\frac{26594 x^3}{3125}-\frac{507023 x^2}{156250}+\frac{1382328 x}{390625}-\frac{1331}{1953125 (5 x+3)}+\frac{19239 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{1944 x^{7}}{175} - \frac{1026 x^{6}}{125} + \frac{44982 x^{5}}{3125} + \frac{108387 x^{4}}{12500} - \frac{26594 x^{3}}{3125} + \frac{19239 \log{\left (5 x + 3 \right )}}{1953125} + \int \frac{1382328}{390625}\, dx - \frac{507023 \int x\, dx}{78125} - \frac{1331}{1953125 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**5/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0537386, size = 66, normalized size = 0.96 \[ \frac{-15187500000 x^8-20334375000 x^7+12946500000 x^6+23662603125 x^5-4521978125 x^4-11417376250 x^3+2176277250 x^2+4982083965 x+2693460 (5 x+3) \log (6 (5 x+3))+1247330759}{273437500 (5 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 52, normalized size = 0.8 \[{\frac{1382328\,x}{390625}}-{\frac{507023\,{x}^{2}}{156250}}-{\frac{26594\,{x}^{3}}{3125}}+{\frac{108387\,{x}^{4}}{12500}}+{\frac{44982\,{x}^{5}}{3125}}-{\frac{1026\,{x}^{6}}{125}}-{\frac{1944\,{x}^{7}}{175}}-{\frac{1331}{5859375+9765625\,x}}+{\frac{19239\,\ln \left ( 3+5\,x \right ) }{1953125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^5/(3+5*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34499, size = 69, normalized size = 1. \[ -\frac{1944}{175} \, x^{7} - \frac{1026}{125} \, x^{6} + \frac{44982}{3125} \, x^{5} + \frac{108387}{12500} \, x^{4} - \frac{26594}{3125} \, x^{3} - \frac{507023}{156250} \, x^{2} + \frac{1382328}{390625} \, x - \frac{1331}{1953125 \,{\left (5 \, x + 3\right )}} + \frac{19239}{1953125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^5*(2*x - 1)^3/(5*x + 3)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215975, size = 84, normalized size = 1.22 \[ -\frac{3037500000 \, x^{8} + 4066875000 \, x^{7} - 2589300000 \, x^{6} - 4732520625 \, x^{5} + 904395625 \, x^{4} + 2283475250 \, x^{3} - 435255450 \, x^{2} - 538692 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 580577760 \, x + 37268}{54687500 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^5*(2*x - 1)^3/(5*x + 3)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.248824, size = 61, normalized size = 0.88 \[ - \frac{1944 x^{7}}{175} - \frac{1026 x^{6}}{125} + \frac{44982 x^{5}}{3125} + \frac{108387 x^{4}}{12500} - \frac{26594 x^{3}}{3125} - \frac{507023 x^{2}}{156250} + \frac{1382328 x}{390625} + \frac{19239 \log{\left (5 x + 3 \right )}}{1953125} - \frac{1331}{9765625 x + 5859375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**5/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.214816, size = 126, normalized size = 1.83 \[ \frac{1}{273437500} \,{\left (5 \, x + 3\right )}^{7}{\left (\frac{672840}{5 \, x + 3} - \frac{3503304}{{\left (5 \, x + 3\right )}^{2}} + \frac{2251305}{{\left (5 \, x + 3\right )}^{3}} + \frac{16557100}{{\left (5 \, x + 3\right )}^{4}} + \frac{20720140}{{\left (5 \, x + 3\right )}^{5}} + \frac{15264480}{{\left (5 \, x + 3\right )}^{6}} - 38880\right )} - \frac{1331}{1953125 \,{\left (5 \, x + 3\right )}} - \frac{19239}{1953125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^5*(2*x - 1)^3/(5*x + 3)^2,x, algorithm="giac")
[Out]