3.1572 \(\int \frac{(2+3 x)^7}{(1-2 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=65 \[ \frac{2187 x^5}{100}+\frac{13851 x^4}{100}+\frac{853659 x^3}{2000}+\frac{18237069 x^2}{20000}+\frac{370109547 x}{200000}+\frac{823543}{1408 (1-2 x)}+\frac{5764801 \log (1-2 x)}{3872}+\frac{\log (5 x+3)}{1890625} \]

[Out]

823543/(1408*(1 - 2*x)) + (370109547*x)/200000 + (18237069*x^2)/20000 + (853659*
x^3)/2000 + (13851*x^4)/100 + (2187*x^5)/100 + (5764801*Log[1 - 2*x])/3872 + Log
[3 + 5*x]/1890625

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Rubi [A]  time = 0.0725296, antiderivative size = 65, 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 \[ \frac{2187 x^5}{100}+\frac{13851 x^4}{100}+\frac{853659 x^3}{2000}+\frac{18237069 x^2}{20000}+\frac{370109547 x}{200000}+\frac{823543}{1408 (1-2 x)}+\frac{5764801 \log (1-2 x)}{3872}+\frac{\log (5 x+3)}{1890625} \]

Antiderivative was successfully verified.

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

[Out]

823543/(1408*(1 - 2*x)) + (370109547*x)/200000 + (18237069*x^2)/20000 + (853659*
x^3)/2000 + (13851*x^4)/100 + (2187*x^5)/100 + (5764801*Log[1 - 2*x])/3872 + Log
[3 + 5*x]/1890625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{2187 x^{5}}{100} + \frac{13851 x^{4}}{100} + \frac{853659 x^{3}}{2000} + \frac{5764801 \log{\left (- 2 x + 1 \right )}}{3872} + \frac{\log{\left (5 x + 3 \right )}}{1890625} + \int \frac{370109547}{200000}\, dx + \frac{18237069 \int x\, dx}{10000} + \frac{823543}{1408 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2187*x**5/100 + 13851*x**4/100 + 853659*x**3/2000 + 5764801*log(-2*x + 1)/3872 +
log(5*x + 3)/1890625 + Integral(370109547/200000, x) + 18237069*Integral(x, x)/
10000 + 823543/(1408*(-2*x + 1))

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Mathematica [A]  time = 0.0599178, size = 60, normalized size = 0.92 \[ \frac{\frac{11 \left (4811400000 x^6+28066500000 x^5+78666390000 x^4+153656514000 x^3+306816622200 x^2-14798867886 x-158719988357\right )}{2 x-1}[phone] \log (5-10 x)+640 \log (5 x+3)}{1210000000} \]

Antiderivative was successfully verified.

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

[Out]

((11*(-158719988357 - 14798867886*x + 306816622200*x^2 + 153656514000*x^3 + 7866
6390000*x^4 + 28066500000*x^5 + 4811400000*x^6))/(-1 + 2*x) + 1801500312500*Log[
5 - 10*x] + 640*Log[3 + 5*x])/1210000000

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Maple [A]  time = 0.013, size = 50, normalized size = 0.8 \[{\frac{2187\,{x}^{5}}{100}}+{\frac{13851\,{x}^{4}}{100}}+{\frac{853659\,{x}^{3}}{2000}}+{\frac{18237069\,{x}^{2}}{20000}}+{\frac{370109547\,x}{200000}}+{\frac{\ln \left ( 3+5\,x \right ) }{1890625}}-{\frac{823543}{-1408+2816\,x}}+{\frac{5764801\,\ln \left ( -1+2\,x \right ) }{3872}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2187/100*x^5+13851/100*x^4+853659/2000*x^3+18237069/20000*x^2+370109547/200000*x
+1/1890625*ln(3+5*x)-823543/1408/(-1+2*x)+5764801/3872*ln(-1+2*x)

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Maxima [A]  time = 1.34368, size = 66, normalized size = 1.02 \[ \frac{2187}{100} \, x^{5} + \frac{13851}{100} \, x^{4} + \frac{853659}{2000} \, x^{3} + \frac{18237069}{20000} \, x^{2} + \frac{370109547}{200000} \, x - \frac{823543}{1408 \,{\left (2 \, x - 1\right )}} + \frac{1}{1890625} \, \log \left (5 \, x + 3\right ) + \frac{5764801}{3872} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2187/100*x^5 + 13851/100*x^4 + 853659/2000*x^3 + 18237069/20000*x^2 + 370109547/
200000*x - 823543/1408/(2*x - 1) + 1/1890625*log(5*x + 3) + 5764801/3872*log(2*x
- 1)

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Fricas [A]  time = 0.214795, size = 88, normalized size = 1.35 \[ \frac{10585080000 \, x^{6} + 61746300000 \, x^{5} + 173066058000 \, x^{4} + 338044330800 \, x^{3} + 674996568840 \, x^{2} + 128 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 360300062500 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 447832551870 \, x - 141546453125}{242000000 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/242000000*(10585080000*x^6 + 61746300000*x^5 + 173066058000*x^4 + 338044330800
*x^3 + 674996568840*x^2 + 128*(2*x - 1)*log(5*x + 3) + 360300062500*(2*x - 1)*lo
g(2*x - 1) - 447832551870*x - 141546453125)/(2*x - 1)

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Sympy [A]  time = 0.34288, size = 56, normalized size = 0.86 \[ \frac{2187 x^{5}}{100} + \frac{13851 x^{4}}{100} + \frac{853659 x^{3}}{2000} + \frac{18237069 x^{2}}{20000} + \frac{370109547 x}{200000} + \frac{5764801 \log{\left (x - \frac{1}{2} \right )}}{3872} + \frac{\log{\left (x + \frac{3}{5} \right )}}{1890625} - \frac{823543}{2816 x - 1408} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2187*x**5/100 + 13851*x**4/100 + 853659*x**3/2000 + 18237069*x**2/20000 + 370109
547*x/200000 + 5764801*log(x - 1/2)/3872 + log(x + 3/5)/1890625 - 823543/(2816*x
- 1408)

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GIAC/XCAS [A]  time = 0.209476, size = 122, normalized size = 1.88 \[ \frac{27}{400000} \,{\left (2 \, x - 1\right )}^{5}{\left (\frac{178875}{2 \, x - 1} + \frac{1404675}{{\left (2 \, x - 1\right )}^{2}} + \frac{6619260}{{\left (2 \, x - 1\right )}^{3}} + \frac{23397131}{{\left (2 \, x - 1\right )}^{4}} + 10125\right )} - \frac{823543}{1408 \,{\left (2 \, x - 1\right )}} - \frac{744421617}{500000} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{1890625} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

27/400000*(2*x - 1)^5*(178875/(2*x - 1) + 1404675/(2*x - 1)^2 + 6619260/(2*x - 1
)^3 + 23397131/(2*x - 1)^4 + 10125) - 823543/1408/(2*x - 1) - 744421617/500000*l
n(1/2*abs(2*x - 1)/(2*x - 1)^2) + 1/1890625*ln(abs(-11/(2*x - 1) - 5))