3.1386 \(\int \frac{(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=76 \[ -\frac{729 x^8}{25}-\frac{37908 x^7}{875}+\frac{12231 x^6}{625}+\frac{774981 x^5}{15625}-\frac{5643 x^4}{3125}-\frac{1836723 x^3}{78125}-\frac{461623 x^2}{390625}+\frac{13880997 x}{1953125}-\frac{1331}{9765625 (5 x+3)}+\frac{23232 \log (5 x+3)}{9765625} \]

[Out]

(13880997*x)/1953125 - (461623*x^2)/390625 - (1836723*x^3)/78125 - (5643*x^4)/31
25 + (774981*x^5)/15625 + (12231*x^6)/625 - (37908*x^7)/875 - (729*x^8)/25 - 133
1/(9765625*(3 + 5*x)) + (23232*Log[3 + 5*x])/9765625

_______________________________________________________________________________________

Rubi [A]  time = 0.0900883, antiderivative size = 76, 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 \[ -\frac{729 x^8}{25}-\frac{37908 x^7}{875}+\frac{12231 x^6}{625}+\frac{774981 x^5}{15625}-\frac{5643 x^4}{3125}-\frac{1836723 x^3}{78125}-\frac{461623 x^2}{390625}+\frac{13880997 x}{1953125}-\frac{1331}{9765625 (5 x+3)}+\frac{23232 \log (5 x+3)}{9765625} \]

Antiderivative was successfully verified.

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

[Out]

(13880997*x)/1953125 - (461623*x^2)/390625 - (1836723*x^3)/78125 - (5643*x^4)/31
25 + (774981*x^5)/15625 + (12231*x^6)/625 - (37908*x^7)/875 - (729*x^8)/25 - 133
1/(9765625*(3 + 5*x)) + (23232*Log[3 + 5*x])/9765625

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{729 x^{8}}{25} - \frac{37908 x^{7}}{875} + \frac{12231 x^{6}}{625} + \frac{774981 x^{5}}{15625} - \frac{5643 x^{4}}{3125} - \frac{1836723 x^{3}}{78125} + \frac{23232 \log{\left (5 x + 3 \right )}}{9765625} + \int \frac{13880997}{1953125}\, dx - \frac{923246 \int x\, dx}{390625} - \frac{1331}{9765625 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729*x**8/25 - 37908*x**7/875 + 12231*x**6/625 + 774981*x**5/15625 - 5643*x**4/3
125 - 1836723*x**3/78125 + 23232*log(5*x + 3)/9765625 + Integral(13880997/195312
5, x) - 923246*Integral(x, x)/390625 - 1331/(9765625*(5*x + 3))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0588497, size = 71, normalized size = 0.93 \[ \frac{-49833984375 x^9-103939453125 x^8-10979296875 x^7+104830031250 x^6+47772112500 x^5-42029925000 x^4-26126590000 x^3+10934112000 x^2+10818777780 x+813120 (5 x+3) \log (6 (5 x+3))[phone]}{341796875 (5 x+3)} \]

Antiderivative was successfully verified.

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

[Out]

(2118706028 + 10818777780*x + 10934112000*x^2 - 26126590000*x^3 - 42029925000*x^
4 + 47772112500*x^5 + 104830031250*x^6 - 10979296875*x^7 - 103939453125*x^8 - 49
833984375*x^9 + 813120*(3 + 5*x)*Log[6*(3 + 5*x)])/(341796875*(3 + 5*x))

_______________________________________________________________________________________

Maple [A]  time = 0.01, size = 57, normalized size = 0.8 \[{\frac{13880997\,x}{1953125}}-{\frac{461623\,{x}^{2}}{390625}}-{\frac{1836723\,{x}^{3}}{78125}}-{\frac{5643\,{x}^{4}}{3125}}+{\frac{774981\,{x}^{5}}{15625}}+{\frac{12231\,{x}^{6}}{625}}-{\frac{37908\,{x}^{7}}{875}}-{\frac{729\,{x}^{8}}{25}}-{\frac{1331}{29296875+48828125\,x}}+{\frac{23232\,\ln \left ( 3+5\,x \right ) }{9765625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

13880997/1953125*x-461623/390625*x^2-1836723/78125*x^3-5643/3125*x^4+774981/1562
5*x^5+12231/625*x^6-37908/875*x^7-729/25*x^8-1331/9765625/(3+5*x)+23232/9765625*
ln(3+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34581, size = 76, normalized size = 1. \[ -\frac{729}{25} \, x^{8} - \frac{37908}{875} \, x^{7} + \frac{12231}{625} \, x^{6} + \frac{774981}{15625} \, x^{5} - \frac{5643}{3125} \, x^{4} - \frac{1836723}{78125} \, x^{3} - \frac{461623}{390625} \, x^{2} + \frac{13880997}{1953125} \, x - \frac{1331}{9765625 \,{\left (5 \, x + 3\right )}} + \frac{23232}{9765625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^6*(2*x - 1)^3/(5*x + 3)^2,x, algorithm="maxima")

[Out]

-729/25*x^8 - 37908/875*x^7 + 12231/625*x^6 + 774981/15625*x^5 - 5643/3125*x^4 -
1836723/78125*x^3 - 461623/390625*x^2 + 13880997/1953125*x - 1331/9765625/(5*x
+ 3) + 23232/9765625*log(5*x + 3)

_______________________________________________________________________________________

Fricas [A]  time = 0.210856, size = 90, normalized size = 1.18 \[ -\frac{9966796875 \, x^{9} + 20787890625 \, x^{8} + 2195859375 \, x^{7} - 20966006250 \, x^{6} - 9554422500 \, x^{5} + 8405985000 \, x^{4} + 5225318000 \, x^{3} - 2186822400 \, x^{2} - 162624 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1457504685 \, x + 9317}{68359375 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^6*(2*x - 1)^3/(5*x + 3)^2,x, algorithm="fricas")

[Out]

-1/68359375*(9966796875*x^9 + 20787890625*x^8 + 2195859375*x^7 - 20966006250*x^6
- 9554422500*x^5 + 8405985000*x^4 + 5225318000*x^3 - 2186822400*x^2 - 162624*(5
*x + 3)*log(5*x + 3) - 1457504685*x + 9317)/(5*x + 3)

_______________________________________________________________________________________

Sympy [A]  time = 0.26183, size = 68, normalized size = 0.89 \[ - \frac{729 x^{8}}{25} - \frac{37908 x^{7}}{875} + \frac{12231 x^{6}}{625} + \frac{774981 x^{5}}{15625} - \frac{5643 x^{4}}{3125} - \frac{1836723 x^{3}}{78125} - \frac{461623 x^{2}}{390625} + \frac{13880997 x}{1953125} + \frac{23232 \log{\left (5 x + 3 \right )}}{9765625} - \frac{1331}{48828125 x + 29296875} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729*x**8/25 - 37908*x**7/875 + 12231*x**6/625 + 774981*x**5/15625 - 5643*x**4/3
125 - 1836723*x**3/78125 - 461623*x**2/390625 + 13880997*x/1953125 + 23232*log(5
*x + 3)/9765625 - 1331/(48828125*x + 29296875)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.211438, size = 138, normalized size = 1.82 \[ \frac{1}{341796875} \,{\left (5 \, x + 3\right )}^{8}{\left (\frac{422820}{5 \, x + 3} - \frac{2021355}{{\left (5 \, x + 3\right )}^{2}} + \frac{474957}{{\left (5 \, x + 3\right )}^{3}} + \frac{9876195}{{\left (5 \, x + 3\right )}^{4}} + \frac{14499345}{{\left (5 \, x + 3\right )}^{5}} + \frac{10904215}{{\left (5 \, x + 3\right )}^{6}} + \frac{5836215}{{\left (5 \, x + 3\right )}^{7}} - 25515\right )} - \frac{1331}{9765625 \,{\left (5 \, x + 3\right )}} - \frac{23232}{9765625} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^6*(2*x - 1)^3/(5*x + 3)^2,x, algorithm="giac")

[Out]

1/341796875*(5*x + 3)^8*(422820/(5*x + 3) - 2021355/(5*x + 3)^2 + 474957/(5*x +
3)^3 + 9876195/(5*x + 3)^4 + 14499345/(5*x + 3)^5 + 10904215/(5*x + 3)^6 + 58362
15/(5*x + 3)^7 - 25515) - 1331/9765625/(5*x + 3) - 23232/9765625*ln(1/5*abs(5*x
+ 3)/(5*x + 3)^2)