Optimal. Leaf size=72 \[ -\frac{648 x^9}{5}-\frac{13851 x^8}{50}-\frac{40338 x^7}{875}+\frac{331713 x^6}{1250}+\frac{2212083 x^5}{15625}-\frac{5848749 x^4}{62500}-\frac{17453753 x^3}{234375}+\frac{11111259 x^2}{781250}+\frac{41666223 x}{1953125}+\frac{1331 \log (5 x+3)}{9765625} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0719971, antiderivative size = 72, 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 \[ -\frac{648 x^9}{5}-\frac{13851 x^8}{50}-\frac{40338 x^7}{875}+\frac{331713 x^6}{1250}+\frac{2212083 x^5}{15625}-\frac{5848749 x^4}{62500}-\frac{17453753 x^3}{234375}+\frac{11111259 x^2}{781250}+\frac{41666223 x}{1953125}+\frac{1331 \log (5 x+3)}{9765625} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{648 x^{9}}{5} - \frac{13851 x^{8}}{50} - \frac{40338 x^{7}}{875} + \frac{331713 x^{6}}{1250} + \frac{2212083 x^{5}}{15625} - \frac{5848749 x^{4}}{62500} - \frac{17453753 x^{3}}{234375} + \frac{1331 \log{\left (5 x + 3 \right )}}{9765625} + \int \frac{41666223}{1953125}\, dx + \frac{11111259 \int x\, dx}{390625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**6/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0250332, size = 57, normalized size = 0.79 \[ \frac{-531562500000 x^9-1136214843750 x^8-189084375000 x^7+1088433281250 x^6+580671787500 x^5-383824153125 x^4-305440677500 x^3+58334109750 x^2+87499068300 x+559020 \log (5 x+3)+18072649071}{4101562500} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 53, normalized size = 0.7 \[{\frac{41666223\,x}{1953125}}+{\frac{11111259\,{x}^{2}}{781250}}-{\frac{17453753\,{x}^{3}}{234375}}-{\frac{5848749\,{x}^{4}}{62500}}+{\frac{2212083\,{x}^{5}}{15625}}+{\frac{331713\,{x}^{6}}{1250}}-{\frac{40338\,{x}^{7}}{875}}-{\frac{13851\,{x}^{8}}{50}}-{\frac{648\,{x}^{9}}{5}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{9765625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^6/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34294, size = 70, normalized size = 0.97 \[ -\frac{648}{5} \, x^{9} - \frac{13851}{50} \, x^{8} - \frac{40338}{875} \, x^{7} + \frac{331713}{1250} \, x^{6} + \frac{2212083}{15625} \, x^{5} - \frac{5848749}{62500} \, x^{4} - \frac{17453753}{234375} \, x^{3} + \frac{11111259}{781250} \, x^{2} + \frac{41666223}{1953125} \, x + \frac{1331}{9765625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6*(2*x - 1)^3/(5*x + 3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.213211, size = 70, normalized size = 0.97 \[ -\frac{648}{5} \, x^{9} - \frac{13851}{50} \, x^{8} - \frac{40338}{875} \, x^{7} + \frac{331713}{1250} \, x^{6} + \frac{2212083}{15625} \, x^{5} - \frac{5848749}{62500} \, x^{4} - \frac{17453753}{234375} \, x^{3} + \frac{11111259}{781250} \, x^{2} + \frac{41666223}{1953125} \, x + \frac{1331}{9765625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6*(2*x - 1)^3/(5*x + 3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.211925, size = 68, normalized size = 0.94 \[ - \frac{648 x^{9}}{5} - \frac{13851 x^{8}}{50} - \frac{40338 x^{7}}{875} + \frac{331713 x^{6}}{1250} + \frac{2212083 x^{5}}{15625} - \frac{5848749 x^{4}}{62500} - \frac{17453753 x^{3}}{234375} + \frac{11111259 x^{2}}{781250} + \frac{41666223 x}{1953125} + \frac{1331 \log{\left (5 x + 3 \right )}}{9765625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**6/(3+5*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21059, size = 72, normalized size = 1. \[ -\frac{648}{5} \, x^{9} - \frac{13851}{50} \, x^{8} - \frac{40338}{875} \, x^{7} + \frac{331713}{1250} \, x^{6} + \frac{2212083}{15625} \, x^{5} - \frac{5848749}{62500} \, x^{4} - \frac{17453753}{234375} \, x^{3} + \frac{11111259}{781250} \, x^{2} + \frac{41666223}{1953125} \, x + \frac{1331}{9765625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6*(2*x - 1)^3/(5*x + 3),x, algorithm="giac")
[Out]