3.1586 \(\int \frac{(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=76 \[ \frac{6561 x^5}{500}+\frac{168399 x^4}{2000}+\frac{2626101 x^3}{10000}+\frac{14171517 x^2}{25000}+\frac{231915717 x}{200000}+\frac{5764801}{15488 (1-2 x)}-\frac{1}{9453125 (5 x+3)}+\frac{79883671 \log (1-2 x)}{85184}+\frac{268 \log (5 x+3)}{103984375} \]

[Out]

5764801/(15488*(1 - 2*x)) + (231915717*x)/200000 + (14171517*x^2)/25000 + (26261
01*x^3)/10000 + (168399*x^4)/2000 + (6561*x^5)/500 - 1/(9453125*(3 + 5*x)) + (79
883671*Log[1 - 2*x])/85184 + (268*Log[3 + 5*x])/103984375

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Rubi [A]  time = 0.0902512, 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 \[ \frac{6561 x^5}{500}+\frac{168399 x^4}{2000}+\frac{2626101 x^3}{10000}+\frac{14171517 x^2}{25000}+\frac{231915717 x}{200000}+\frac{5764801}{15488 (1-2 x)}-\frac{1}{9453125 (5 x+3)}+\frac{79883671 \log (1-2 x)}{85184}+\frac{268 \log (5 x+3)}{103984375} \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^2),x]

[Out]

5764801/(15488*(1 - 2*x)) + (231915717*x)/200000 + (14171517*x^2)/25000 + (26261
01*x^3)/10000 + (168399*x^4)/2000 + (6561*x^5)/500 - 1/(9453125*(3 + 5*x)) + (79
883671*Log[1 - 2*x])/85184 + (268*Log[3 + 5*x])/103984375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{6561 x^{5}}{500} + \frac{168399 x^{4}}{2000} + \frac{2626101 x^{3}}{10000} + \frac{79883671 \log{\left (- 2 x + 1 \right )}}{85184} + \frac{268 \log{\left (5 x + 3 \right )}}{103984375} + \int \frac{231915717}{200000}\, dx + \frac{14171517 \int x\, dx}{12500} - \frac{1}{9453125 \left (5 x + 3\right )} + \frac{5764801}{15488 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**8/(1-2*x)**2/(3+5*x)**2,x)

[Out]

6561*x**5/500 + 168399*x**4/2000 + 2626101*x**3/10000 + 79883671*log(-2*x + 1)/8
5184 + 268*log(5*x + 3)/103984375 + Integral(231915717/200000, x) + 14171517*Int
egral(x, x)/12500 - 1/(9453125*(5*x + 3)) + 5764801/(15488*(-2*x + 1))

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Mathematica [A]  time = 0.072135, size = 95, normalized size = 1.25 \[ -\frac{2251875390881 x+1351125234247}{1210000000 \left (10 x^2+x-3\right )}+\frac{27}{500} (3 x+2)^5+\frac{999 (3 x+2)^4}{2000}+\frac{35703 (3 x+2)^3}{10000}+\frac{78921 (3 x+2)^2}{3125}+\frac{44471943 (3 x+2)}{200000}+\frac{79883671 \log (3-6 x)}{85184}+\frac{268 \log (-3 (5 x+3))}{103984375} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^2),x]

[Out]

(44471943*(2 + 3*x))/200000 + (78921*(2 + 3*x)^2)/3125 + (35703*(2 + 3*x)^3)/100
00 + (999*(2 + 3*x)^4)/2000 + (27*(2 + 3*x)^5)/500 - (1351125234247 + 2251875390
881*x)/(1210000000*(-3 + x + 10*x^2)) + (79883671*Log[3 - 6*x])/85184 + (268*Log
[-3*(3 + 5*x)])/103984375

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Maple [A]  time = 0.014, size = 59, normalized size = 0.8 \[{\frac{6561\,{x}^{5}}{500}}+{\frac{168399\,{x}^{4}}{2000}}+{\frac{2626101\,{x}^{3}}{10000}}+{\frac{14171517\,{x}^{2}}{25000}}+{\frac{231915717\,x}{200000}}-{\frac{1}{28359375+47265625\,x}}+{\frac{268\,\ln \left ( 3+5\,x \right ) }{103984375}}-{\frac{5764801}{-15488+30976\,x}}+{\frac{79883671\,\ln \left ( -1+2\,x \right ) }{85184}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^8/(1-2*x)^2/(3+5*x)^2,x)

[Out]

6561/500*x^5+168399/2000*x^4+2626101/10000*x^3+14171517/25000*x^2+231915717/2000
00*x-1/9453125/(3+5*x)+268/103984375*ln(3+5*x)-5764801/15488/(-1+2*x)[phone]/8
5184*ln(-1+2*x)

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Maxima [A]  time = 1.33321, size = 77, normalized size = 1.01 \[ \frac{6561}{500} \, x^{5} + \frac{168399}{2000} \, x^{4} + \frac{2626101}{10000} \, x^{3} + \frac{14171517}{25000} \, x^{2} + \frac{231915717}{200000} \, x - \frac{2251875390881 \, x + 1351125234247}{1210000000 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{268}{103984375} \, \log \left (5 \, x + 3\right ) + \frac{79883671}{85184} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^8/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="maxima")

[Out]

6561/500*x^5 + 168399/2000*x^4 + 2626101/10000*x^3 + 14171517/25000*x^2 + 231915
717/200000*x - 1/1210000000*(2251875390881*x + 1351125234247)/(10*x^2 + x - 3) +
268/103984375*log(5*x + 3) + 79883671/85184*log(2*x - 1)

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Fricas [A]  time = 0.211009, size = 107, normalized size = 1.41 \[ \frac{1746538200000 \, x^{7} + 11381607270000 \, x^{6} + 35550138195000 \, x^{5} + 75582410904000 \, x^{4} + 151398804021300 \, x^{3} - 7200755986050 \, x^{2} + 34304 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 12481823593750 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 71072602198741 \, x - 14862377576717}{13310000000 \,{\left (10 \, x^{2} + x - 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^8/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="fricas")

[Out]

1/13310000000*(1746538200000*x^7 + 11381607270000*x^6 + 35550138195000*x^5 + 755
82410904000*x^4 + 151398804021300*x^3 - 7200755986050*x^2 + 34304*(10*x^2 + x -
3)*log(5*x + 3) + 12481823593750*(10*x^2 + x - 3)*log(2*x - 1) - 71072602198741*
x - 14862377576717)/(10*x^2 + x - 3)

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Sympy [A]  time = 0.421417, size = 66, normalized size = 0.87 \[ \frac{6561 x^{5}}{500} + \frac{168399 x^{4}}{2000} + \frac{2626101 x^{3}}{10000} + \frac{14171517 x^{2}}{25000} + \frac{231915717 x}{200000} - \frac{2251875390881 x + 1351125234247}{12100000000 x^{2} + 1210000000 x - 3630000000} + \frac{79883671 \log{\left (x - \frac{1}{2} \right )}}{85184} + \frac{268 \log{\left (x + \frac{3}{5} \right )}}{103984375} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**8/(1-2*x)**2/(3+5*x)**2,x)

[Out]

6561*x**5/500 + 168399*x**4/2000 + 2626101*x**3/10000 + 14171517*x**2/25000 + 23
1915717*x/200000 - (2251875390881*x + 1351125234247)/(12100000000*x**2 + 1210000
000*x - 3630000000) + 79883671*log(x - 1/2)/85184 + 268*log(x + 3/5)/103984375

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GIAC/XCAS [A]  time = 0.20915, size = 151, normalized size = 1.99 \[ -\frac{{\left (5 \, x + 3\right )}^{5}{\left (\frac{1618458732}{5 \, x + 3} + \frac{15560361630}{{\left (5 \, x + 3\right )}^{2}} + \frac{171888467850}{{\left (5 \, x + 3\right )}^{3}} + \frac{2836763461125}{{\left (5 \, x + 3\right )}^{4}} - \frac{31204564033975}{{\left (5 \, x + 3\right )}^{5}} + 139723056\right )}}{16637500000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{1}{9453125 \,{\left (5 \, x + 3\right )}} - \frac{4688889417}{5000000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{79883671}{85184} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^8/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="giac")

[Out]

-1/16637500000*(5*x + 3)^5*(1618458732/(5*x + 3) + 15560361630/(5*x + 3)^2 + 171
888467850/(5*x + 3)^3 + 2836763461125/(5*x + 3)^4 - 31204564033975/(5*x + 3)^5 +
139723056)/(11/(5*x + 3) - 2) - 1/9453125/(5*x + 3) - 4688889417/5000000*ln(1/5
*abs(5*x + 3)/(5*x + 3)^2) + 79883671/85184*ln(abs(-11/(5*x + 3) + 2))