3.1601 \(\int \frac{(2+3 x)^7}{(1-2 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=73 \[ \frac{729 x^3}{500}+\frac{21141 x^2}{2500}+\frac{1467477 x}{50000}+\frac{823543}{42592 (1-2 x)}-\frac{47}{4159375 (5 x+3)}-\frac{1}{3781250 (5 x+3)^2}+\frac{7411887 \log (1-2 x)}{234256}+\frac{4761 \log (5 x+3)}{45753125} \]

[Out]

823543/(42592*(1 - 2*x)) + (1467477*x)/50000 + (21141*x^2)/2500 + (729*x^3)/500
- 1/(3781250*(3 + 5*x)^2) - 47/(4159375*(3 + 5*x)) + (7411887*Log[1 - 2*x])/2342
56 + (4761*Log[3 + 5*x])/45753125

_______________________________________________________________________________________

Rubi [A]  time = 0.0885079, antiderivative size = 73, 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 \[ \frac{729 x^3}{500}+\frac{21141 x^2}{2500}+\frac{1467477 x}{50000}+\frac{823543}{42592 (1-2 x)}-\frac{47}{4159375 (5 x+3)}-\frac{1}{3781250 (5 x+3)^2}+\frac{7411887 \log (1-2 x)}{234256}+\frac{4761 \log (5 x+3)}{45753125} \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^3),x]

[Out]

823543/(42592*(1 - 2*x)) + (1467477*x)/50000 + (21141*x^2)/2500 + (729*x^3)/500
- 1/(3781250*(3 + 5*x)^2) - 47/(4159375*(3 + 5*x)) + (7411887*Log[1 - 2*x])/2342
56 + (4761*Log[3 + 5*x])/45753125

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{729 x^{3}}{500} + \frac{7411887 \log{\left (- 2 x + 1 \right )}}{234256} + \frac{4761 \log{\left (5 x + 3 \right )}}{45753125} + \int \frac{1467477}{50000}\, dx + \frac{21141 \int x\, dx}{1250} - \frac{47}{4159375 \left (5 x + 3\right )} - \frac{1}{3781250 \left (5 x + 3\right )^{2}} + \frac{823543}{42592 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**7/(1-2*x)**2/(3+5*x)**3,x)

[Out]

729*x**3/500 + 7411887*log(-2*x + 1)/234256 + 4761*log(5*x + 3)/45753125 + Integ
ral(1467477/50000, x) + 21141*Integral(x, x)/1250 - 47/(4159375*(5*x + 3)) - 1/(
3781250*(5*x + 3)**2) + 823543/(42592*(-2*x + 1))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0733078, size = 67, normalized size = 0.92 \[ \frac{\frac{11 \left (48514950000 x^6+315347175000 x^5+1161933052500 x^4+42644641050 x^3-1002031406415 x^2-426293494632 x-14162188399\right )}{(2 x-1) (5 x+3)^2}[phone] \log (1-2 x)+761760 \log (10 x+6)}{7320500000} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^3),x]

[Out]

((11*(-14162188399 - 426293494632*x - 1002031406415*x^2 + 42644641050*x^3 + 1161
933052500*x^4 + 315347175000*x^5 + 48514950000*x^6))/((-1 + 2*x)*(3 + 5*x)^2) +
231621468750*Log[1 - 2*x] + 761760*Log[6 + 10*x])/7320500000

_______________________________________________________________________________________

Maple [A]  time = 0.016, size = 58, normalized size = 0.8 \[{\frac{729\,{x}^{3}}{500}}+{\frac{21141\,{x}^{2}}{2500}}+{\frac{1467477\,x}{50000}}-{\frac{1}{3781250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{47}{12478125+20796875\,x}}+{\frac{4761\,\ln \left ( 3+5\,x \right ) }{45753125}}-{\frac{823543}{-42592+85184\,x}}+{\frac{7411887\,\ln \left ( -1+2\,x \right ) }{234256}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^7/(1-2*x)^2/(3+5*x)^3,x)

[Out]

729/500*x^3+21141/2500*x^2+1467477/50000*x-1/3781250/(3+5*x)^2-47/4159375/(3+5*x
)+4761/45753125*ln(3+5*x)-823543/42592/(-1+2*x)+7411887/234256*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34909, size = 80, normalized size = 1.1 \[ \frac{729}{500} \, x^{3} + \frac{21141}{2500} \, x^{2} + \frac{1467477}{50000} \, x - \frac{321696559575 \, x^{2} + 386035789122 \, x + 115810711639}{665500000 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{4761}{45753125} \, \log \left (5 \, x + 3\right ) + \frac{7411887}{234256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^7/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="maxima")

[Out]

729/500*x^3 + 21141/2500*x^2 + 1467477/50000*x - 1/665500000*(321696559575*x^2 +
386035789122*x + 115810711639)/(50*x^3 + 35*x^2 - 12*x - 9) + 4761/45753125*log
(5*x + 3) + 7411887/234256*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.216498, size = 128, normalized size = 1.75 \[ \frac{533664450000 \, x^{6} + 3468818925000 \, x^{5} + 12781263577500 \, x^{4} + 6680945249550 \, x^{3} - 6674047531965 \, x^{2} + 761760 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 231621468750 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) - 6180073448472 \, x - 1273917828029}{7320500000 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^7/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="fricas")

[Out]

1/7320500000*(533664450000*x^6 + 3468818925000*x^5 + 12781263577500*x^4 + 668094
5249550*x^3 - 6674047531965*x^2 + 761760*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x +
3) + 231621468750*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) - 6180073448472*x -
1273917828029)/(50*x^3 + 35*x^2 - 12*x - 9)

_______________________________________________________________________________________

Sympy [A]  time = 0.494464, size = 63, normalized size = 0.86 \[ \frac{729 x^{3}}{500} + \frac{21141 x^{2}}{2500} + \frac{1467477 x}{50000} - \frac{321696559575 x^{2} + 386035789122 x + 115810711639}{33275000000 x^{3} + 23292500000 x^{2} - 7986000000 x - 5989500000} + \frac{7411887 \log{\left (x - \frac{1}{2} \right )}}{234256} + \frac{4761 \log{\left (x + \frac{3}{5} \right )}}{45753125} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**7/(1-2*x)**2/(3+5*x)**3,x)

[Out]

729*x**3/500 + 21141*x**2/2500 + 1467477*x/50000 - (321696559575*x**2 + 38603578
9122*x + 115810711639)/(33275000000*x**3 + 23292500000*x**2 - 7986000000*x - 598
9500000) + 7411887*log(x - 1/2)/234256 + 4761*log(x + 3/5)/45753125

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.212098, size = 139, normalized size = 1.9 \[ \frac{{\left (2 \, x - 1\right )}^{3}{\left (\frac{25349061375}{2 \, x - 1} + \frac{234545525775}{{\left (2 \, x - 1\right )}^{2}} + \frac{720756547985}{{\left (2 \, x - 1\right )}^{3}} + \frac{689127341628}{{\left (2 \, x - 1\right )}^{4}} + 1334161125\right )}}{292820000 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} - \frac{823543}{42592 \,{\left (2 \, x - 1\right )}} - \frac{1582011}{50000} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{4761}{45753125} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^7/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="giac")

[Out]

1/292820000*(2*x - 1)^3*(25349061375/(2*x - 1) + 234545525775/(2*x - 1)^2 + 7207
56547985/(2*x - 1)^3 + 689127341628/(2*x - 1)^4 + 1334161125)/(11/(2*x - 1) + 5)
^2 - 823543/42592/(2*x - 1) - 1582011/50000*ln(1/2*abs(2*x - 1)/(2*x - 1)^2) + 4
761/45753125*ln(abs(-11/(2*x - 1) - 5))