3.1571 \(\int \frac{(2+3 x)^8}{(1-2 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=72 \[ \frac{2187 x^6}{40}+\frac{94041 x^5}{250}+\frac{9899091 x^4}{8000}+\frac{26773659 x^3}{10000}+\frac{1839811401 x^2}{400000}+\frac{2041906293 x}{250000}+\frac{5764801}{2816 (1-2 x)}+\frac{188591347 \log (1-2 x)}{30976}+\frac{\log (5 x+3)}{9453125} \]

[Out]

5764801/(2816*(1 - 2*x)) + (2041906293*x)/250000 + (1839811401*x^2)/400000 + (26
773659*x^3)/10000 + (9899091*x^4)/8000 + (94041*x^5)/250 + (2187*x^6)/40 + (1885
91347*Log[1 - 2*x])/30976 + Log[3 + 5*x]/9453125

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Rubi [A]  time = 0.0808875, 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 \[ \frac{2187 x^6}{40}+\frac{94041 x^5}{250}+\frac{9899091 x^4}{8000}+\frac{26773659 x^3}{10000}+\frac{1839811401 x^2}{400000}+\frac{2041906293 x}{250000}+\frac{5764801}{2816 (1-2 x)}+\frac{188591347 \log (1-2 x)}{30976}+\frac{\log (5 x+3)}{9453125} \]

Antiderivative was successfully verified.

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

[Out]

5764801/(2816*(1 - 2*x)) + (2041906293*x)/250000 + (1839811401*x^2)/400000 + (26
773659*x^3)/10000 + (9899091*x^4)/8000 + (94041*x^5)/250 + (2187*x^6)/40 + (1885
91347*Log[1 - 2*x])/30976 + Log[3 + 5*x]/9453125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{2187 x^{6}}{40} + \frac{94041 x^{5}}{250} + \frac{9899091 x^{4}}{8000} + \frac{26773659 x^{3}}{10000} + \frac{188591347 \log{\left (- 2 x + 1 \right )}}{30976} + \frac{\log{\left (5 x + 3 \right )}}{9453125} + \int \frac{2041906293}{250000}\, dx + \frac{1839811401 \int x\, dx}{200000} + \frac{5764801}{2816 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2187*x**6/40 + 94041*x**5/250 + 9899091*x**4/8000 + 26773659*x**3/10000 + 188591
347*log(-2*x + 1)/30976 + log(5*x + 3)/9453125 + Integral(2041906293/250000, x)
+ 1839811401*Integral(x, x)/200000 + 5764801/(2816*(-2*x + 1))

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Mathematica [A]  time = 0.11178, size = 66, normalized size = 0.92 \[ \frac{109350000 x^6+752328000 x^5+2474772750 x^4+5354731800 x^3+9199057005 x^2+16335250344 x+\frac{90075015625}{22-44 x}[phone]}{2000000}+\frac{188591347 \log (3-6 x)}{30976}+\frac{\log (-3 (5 x+3))}{9453125} \]

Antiderivative was successfully verified.

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

[Out]

(7988912316 + 90075015625/(22 - 44*x) + 16335250344*x + 9199057005*x^2 + 5354731
800*x^3 + 2474772750*x^4 + 752328000*x^5 + 109350000*x^6)/2000000 + (188591347*L
og[3 - 6*x])/30976 + Log[-3*(3 + 5*x)]/9453125

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Maple [A]  time = 0.013, size = 55, normalized size = 0.8 \[{\frac{2187\,{x}^{6}}{40}}+{\frac{94041\,{x}^{5}}{250}}+{\frac{9899091\,{x}^{4}}{8000}}+{\frac{26773659\,{x}^{3}}{10000}}+{\frac{1839811401\,{x}^{2}}{400000}}+{\frac{2041906293\,x}{250000}}+{\frac{\ln \left ( 3+5\,x \right ) }{9453125}}-{\frac{5764801}{-2816+5632\,x}}+{\frac{188591347\,\ln \left ( -1+2\,x \right ) }{30976}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2187/40*x^6+94041/250*x^5+9899091/8000*x^4+26773659/10000*x^3+1839811401/400000*
x^2+2041906293/250000*x+1/9453125*ln(3+5*x)-5764801/2816/(-1+2*x)[phone]/3097
6*ln(-1+2*x)

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Maxima [A]  time = 1.34674, size = 73, normalized size = 1.01 \[ \frac{2187}{40} \, x^{6} + \frac{94041}{250} \, x^{5} + \frac{9899091}{8000} \, x^{4} + \frac{26773659}{10000} \, x^{3} + \frac{1839811401}{400000} \, x^{2} + \frac{2041906293}{250000} \, x - \frac{5764801}{2816 \,{\left (2 \, x - 1\right )}} + \frac{1}{9453125} \, \log \left (5 \, x + 3\right ) + \frac{188591347}{30976} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2187/40*x^6 + 94041/250*x^5 + 9899091/8000*x^4 + 26773659/10000*x^3 + 1839811401
/400000*x^2 + 2041906293/250000*x - 5764801/2816/(2*x - 1) + 1/9453125*log(5*x +
3) + 188591347/30976*log(2*x - 1)

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Fricas [A]  time = 0.217911, size = 95, normalized size = 1.32 \[ \frac{264627000000 \, x^{7} + 1688320260000 \, x^{6} + 5078633175000 \, x^{5} + 9963975928500 \, x^{4} + 15782492474100 \, x^{3} + 28400446856430 \, x^{2} + 256 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 14733698984375 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 19765652916240 \, x - 4954125859375}{2420000000 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2420000000*(264627000000*x^7 + 1688320260000*x^6 + 5078633175000*x^5 + 9963975
928500*x^4 + 15782492474100*x^3 + 28400446856430*x^2 + 256*(2*x - 1)*log(5*x + 3
) + 14733698984375*(2*x - 1)*log(2*x - 1) - 19765652916240*x - 4954125859375)/(2
*x - 1)

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Sympy [A]  time = 0.376997, size = 63, normalized size = 0.88 \[ \frac{2187 x^{6}}{40} + \frac{94041 x^{5}}{250} + \frac{9899091 x^{4}}{8000} + \frac{26773659 x^{3}}{10000} + \frac{1839811401 x^{2}}{400000} + \frac{2041906293 x}{250000} + \frac{188591347 \log{\left (x - \frac{1}{2} \right )}}{30976} + \frac{\log{\left (x + \frac{3}{5} \right )}}{9453125} - \frac{5764801}{5632 x - 2816} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2187*x**6/40 + 94041*x**5/250 + 9899091*x**4/8000 + 26773659*x**3/10000 + 183981
1401*x**2/400000 + 2041906293*x/250000 + 188591347*log(x - 1/2)/30976 + log(x +
3/5)/9453125 - 5764801/(5632*x - 2816)

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GIAC/XCAS [A]  time = 0.208276, size = 134, normalized size = 1.86 \[ \frac{27}{16000000} \,{\left (2 \, x - 1\right )}^{6}{\left (\frac{10003500}{2 \, x - 1} + \frac{88252875}{{\left (2 \, x - 1\right )}^{2}} + \frac{461424900}{{\left (2 \, x - 1\right )}^{3}} + \frac{1628610330}{{\left (2 \, x - 1\right )}^{4}} + \frac{4599014548}{{\left (2 \, x - 1\right )}^{5}} + 506250\right )} - \frac{5764801}{2816 \,{\left (2 \, x - 1\right )}} - \frac{121766107311}{20000000} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{9453125} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

27/16000000*(2*x - 1)^6*(10003500/(2*x - 1) + 88252875/(2*x - 1)^2 + 461424900/(
2*x - 1)^3 + 1628610330/(2*x - 1)^4 + 4599014548/(2*x - 1)^5 + 506250) - 5764801
/2816/(2*x - 1) - 121766107311/20000000*ln(1/2*abs(2*x - 1)/(2*x - 1)^2) + 1/945
3125*ln(abs(-11/(2*x - 1) - 5))