3.1371 \(\int \frac{(1-2 x)^3 (2+3 x)^6}{3+5 x} \, dx\)

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]

(41666223*x)/1953125 + (11111259*x^2)/781250 - (17453753*x^3)/234375 - (5848749*
x^4)/62500 + (2212083*x^5)/15625 + (331713*x^6)/1250 - (40338*x^7)/875 - (13851*
x^8)/50 - (648*x^9)/5 + (1331*Log[3 + 5*x])/9765625

_______________________________________________________________________________________

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]

(41666223*x)/1953125 + (11111259*x^2)/781250 - (17453753*x^3)/234375 - (5848749*
x^4)/62500 + (2212083*x^5)/15625 + (331713*x^6)/1250 - (40338*x^7)/875 - (13851*
x^8)/50 - (648*x^9)/5 + (1331*Log[3 + 5*x])/9765625

_______________________________________________________________________________________

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]

-648*x**9/5 - 13851*x**8/50 - 40338*x**7/875 + 331713*x**6/1250 + 2212083*x**5/1
5625 - 5848749*x**4/62500 - 17453753*x**3/234375 + 1331*log(5*x + 3)/9765625 + I
ntegral(41666223/1953125, x) + 11111259*Integral(x, x)/390625

_______________________________________________________________________________________

Mathematica [A]  time = 0.0250332, size = 57, normalized size = 0.79 \[ \frac{-531562500000 x^9-1136214843750 x^8-189084375000 x^7+1088433281250 x^6+580671787500 x^5-383824153125 x^4-305440677500 x^3+58334109750 x^2+87499068300 x+559020 \log (5 x+3)[phone]}{4101562500} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x),x]

[Out]

(18072649071 + 87499068300*x + 58334109750*x^2 - 305440677500*x^3 - 383824153125
*x^4 + 580671787500*x^5 + 1088433281250*x^6 - 189084375000*x^7 - 1136214843750*x
^8 - 531562500000*x^9 + 559020*Log[3 + 5*x])/4101562500

_______________________________________________________________________________________

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]

41666223/1953125*x+11111259/781250*x^2-17453753/234375*x^3-5848749/62500*x^4+221
2083/15625*x^5+331713/1250*x^6-40338/875*x^7-13851/50*x^8-648/5*x^9+1331/9765625
*ln(3+5*x)

_______________________________________________________________________________________

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]

-648/5*x^9 - 13851/50*x^8 - 40338/875*x^7 + 331713/1250*x^6 + 2212083/15625*x^5
- 5848749/62500*x^4 - 17453753/234375*x^3 + 11111259/781250*x^2 + 41666223/19531
25*x + 1331/9765625*log(5*x + 3)

_______________________________________________________________________________________

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]

-648/5*x^9 - 13851/50*x^8 - 40338/875*x^7 + 331713/1250*x^6 + 2212083/15625*x^5
- 5848749/62500*x^4 - 17453753/234375*x^3 + 11111259/781250*x^2 + 41666223/19531
25*x + 1331/9765625*log(5*x + 3)

_______________________________________________________________________________________

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]

-648*x**9/5 - 13851*x**8/50 - 40338*x**7/875 + 331713*x**6/1250 + 2212083*x**5/1
5625 - 5848749*x**4/62500 - 17453753*x**3/234375 + 11111259*x**2/781250 + 416662
23*x/1953125 + 1331*log(5*x + 3)/9765625

_______________________________________________________________________________________

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]

-648/5*x^9 - 13851/50*x^8 - 40338/875*x^7 + 331713/1250*x^6 + 2212083/15625*x^5
- 5848749/62500*x^4 - 17453753/234375*x^3 + 11111259/781250*x^2 + 41666223/19531
25*x + 1331/9765625*ln(abs(5*x + 3))