3.1668 \(\int \frac{(2+3 x)^7}{(1-2 x)^3 (3+5 x)^2} \, dx\)

Optimal. Leaf size=73 \[ -\frac{729 x^3}{200}-\frac{108621 x^2}{4000}-\frac{1258983 x}{10000}-\frac{18941489}{85184 (1-2 x)}-\frac{1}{4159375 (5 x+3)}+\frac{823543}{15488 (1-2 x)^2}-\frac{87177909 \log (1-2 x)}{468512}+\frac{237 \log (5 x+3)}{45753125} \]

[Out]

823543/(15488*(1 - 2*x)^2) - 18941489/(85184*(1 - 2*x)) - (1258983*x)/10000 - (1
08621*x^2)/4000 - (729*x^3)/200 - 1/(4159375*(3 + 5*x)) - (87177909*Log[1 - 2*x]
)/468512 + (237*Log[3 + 5*x])/45753125

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Rubi [A]  time = 0.0879544, 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 \[ -\frac{729 x^3}{200}-\frac{108621 x^2}{4000}-\frac{1258983 x}{10000}-\frac{18941489}{85184 (1-2 x)}-\frac{1}{4159375 (5 x+3)}+\frac{823543}{15488 (1-2 x)^2}-\frac{87177909 \log (1-2 x)}{468512}+\frac{237 \log (5 x+3)}{45753125} \]

Antiderivative was successfully verified.

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

[Out]

823543/(15488*(1 - 2*x)^2) - 18941489/(85184*(1 - 2*x)) - (1258983*x)/10000 - (1
08621*x^2)/4000 - (729*x^3)/200 - 1/(4159375*(3 + 5*x)) - (87177909*Log[1 - 2*x]
)/468512 + (237*Log[3 + 5*x])/45753125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{729 x^{3}}{200} - \frac{87177909 \log{\left (- 2 x + 1 \right )}}{468512} + \frac{237 \log{\left (5 x + 3 \right )}}{45753125} + \int \left (- \frac{1258983}{10000}\right )\, dx - \frac{108621 \int x\, dx}{2000} - \frac{1}{4159375 \left (5 x + 3\right )} - \frac{18941489}{85184 \left (- 2 x + 1\right )} + \frac{823543}{15488 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729*x**3/200 - 87177909*log(-2*x + 1)/468512 + 237*log(5*x + 3)/45753125 + Inte
gral(-1258983/10000, x) - 108621*Integral(x, x)/2000 - 1/(4159375*(5*x + 3)) - 1
8941489/(85184*(-2*x + 1)) + 823543/(15488*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0788707, size = 67, normalized size = 0.92 \[ \frac{-\frac{22 \left (4851495000 x^6+34203039750 x^5+151415158950 x^4-172378468845 x^3-163837494156 x^2+25343933346 x+19763981131\right )}{(1-2 x)^2 (5 x+3)}-272430965625 \log (1-2 x)+7584 \log (10 x+6)}{1464100000} \]

Antiderivative was successfully verified.

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

[Out]

((-22*(19763981131 + 25343933346*x - 163837494156*x^2 - 172378468845*x^3 + 15141
5158950*x^4 + 34203039750*x^5 + 4851495000*x^6))/((1 - 2*x)^2*(3 + 5*x)) - 27243
0965625*Log[1 - 2*x] + 7584*Log[6 + 10*x])/1464100000

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Maple [A]  time = 0.014, size = 58, normalized size = 0.8 \[ -{\frac{729\,{x}^{3}}{200}}-{\frac{108621\,{x}^{2}}{4000}}-{\frac{1258983\,x}{10000}}-{\frac{1}{12478125+20796875\,x}}+{\frac{237\,\ln \left ( 3+5\,x \right ) }{45753125}}+{\frac{823543}{15488\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{18941489}{-85184+170368\,x}}-{\frac{87177909\,\ln \left ( -1+2\,x \right ) }{468512}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729/200*x^3-108621/4000*x^2-1258983/10000*x-1/4159375/(3+5*x)+237/45753125*ln(3
+5*x)+823543/15488/(-1+2*x)^2+18941489/85184/(-1+2*x)-87177909/468512*ln(-1+2*x)

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Maxima [A]  time = 1.33961, size = 80, normalized size = 1.1 \[ -\frac{729}{200} \, x^{3} - \frac{108621}{4000} \, x^{2} - \frac{1258983}{10000} \, x + \frac{1183843061988 \, x^{2} + 259930759887 \, x - 270225047003}{532400000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{237}{45753125} \, \log \left (5 \, x + 3\right ) - \frac{87177909}{468512} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729/200*x^3 - 108621/4000*x^2 - 1258983/10000*x + 1/532400000*(1183843061988*x^
2 + 259930759887*x - 270225047003)/(20*x^3 - 8*x^2 - 7*x + 3) + 237/45753125*log
(5*x + 3) - 87177909/468512*log(2*x - 1)

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Fricas [A]  time = 0.20975, size = 128, normalized size = 1.75 \[ -\frac{426931560000 \, x^{6} + 3009867498000 \, x^{5} + 13324533987600 \, x^{4} - 6947670741660 \, x^{3} - 17706353292408 \, x^{2} - 30336 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 1089723862500 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 647305946397 \, x + 2972475517033}{5856400000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/5856400000*(426931560000*x^6 + 3009867498000*x^5 + 13324533987600*x^4 - 69476
70741660*x^3 - 17706353292408*x^2 - 30336*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3
) + 1089723862500*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) - 647305946397*x + 297
2475517033)/(20*x^3 - 8*x^2 - 7*x + 3)

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Sympy [A]  time = 0.534817, size = 63, normalized size = 0.86 \[ - \frac{729 x^{3}}{200} - \frac{108621 x^{2}}{4000} - \frac{1258983 x}{10000} + \frac{1183843061988 x^{2} + 259930759887 x - 270225047003}{10648000000 x^{3} - 4259200000 x^{2} - 3726800000 x + 1597200000} - \frac{87177909 \log{\left (x - \frac{1}{2} \right )}}{468512} + \frac{237 \log{\left (x + \frac{3}{5} \right )}}{45753125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729*x**3/200 - 108621*x**2/4000 - 1258983*x/10000 + (1183843061988*x**2 + 25993
0759887*x - 270225047003)/(10648000000*x**3 - 4259200000*x**2 - 3726800000*x + 1
597200000) - 87177909*log(x - 1/2)/468512 + 237*log(x + 3/5)/45753125

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GIAC/XCAS [A]  time = 0.221194, size = 139, normalized size = 1.9 \[ -\frac{{\left (5 \, x + 3\right )}^{3}{\left (\frac{1472913882}{5 \, x + 3} + \frac{33001809588}{{\left (5 \, x + 3\right )}^{2}} - \frac{817302548083}{{\left (5 \, x + 3\right )}^{3}} + \frac{2996736348771}{{\left (5 \, x + 3\right )}^{4}} + 85386312\right )}}{732050000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{1}{4159375 \,{\left (5 \, x + 3\right )}} + \frac{18607401}{100000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{87177909}{468512} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/732050000*(5*x + 3)^3*(1472913882/(5*x + 3) + 33001809588/(5*x + 3)^2 - 81730
2548083/(5*x + 3)^3 + 2996736348771/(5*x + 3)^4 + 85386312)/(11/(5*x + 3) - 2)^2
- 1/4159375/(5*x + 3) + 18607401/100000*ln(1/5*abs(5*x + 3)/(5*x + 3)^2) - 8717
7909/468512*ln(abs(-11/(5*x + 3) + 2))