3.1590 \(\int \frac{(2+3 x)^4}{(1-2 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=48 \[ \frac{81 x}{100}+\frac{2401}{968 (1-2 x)}-\frac{1}{15125 (5 x+3)}+\frac{10633 \log (1-2 x)}{5324}+\frac{136 \log (5 x+3)}{166375} \]

[Out]

2401/(968*(1 - 2*x)) + (81*x)/100 - 1/(15125*(3 + 5*x)) + (10633*Log[1 - 2*x])/5
324 + (136*Log[3 + 5*x])/166375

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Rubi [A]  time = 0.0568725, antiderivative size = 48, 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 \[ \frac{81 x}{100}+\frac{2401}{968 (1-2 x)}-\frac{1}{15125 (5 x+3)}+\frac{10633 \log (1-2 x)}{5324}+\frac{136 \log (5 x+3)}{166375} \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)^2),x]

[Out]

2401/(968*(1 - 2*x)) + (81*x)/100 - 1/(15125*(3 + 5*x)) + (10633*Log[1 - 2*x])/5
324 + (136*Log[3 + 5*x])/166375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{10633 \log{\left (- 2 x + 1 \right )}}{5324} + \frac{136 \log{\left (5 x + 3 \right )}}{166375} + \int \frac{81}{100}\, dx - \frac{1}{15125 \left (5 x + 3\right )} + \frac{2401}{968 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**4/(1-2*x)**2/(3+5*x)**2,x)

[Out]

10633*log(-2*x + 1)/5324 + 136*log(5*x + 3)/166375 + Integral(81/100, x) - 1/(15
125*(5*x + 3)) + 2401/(968*(-2*x + 1))

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Mathematica [A]  time = 0.0564181, size = 47, normalized size = 0.98 \[ \frac{-\frac{11 (1500641 x+900367)}{10 x^2+x-3}+359370 (3 x+2)+2658250 \log (3-6 x)+1088 \log (-3 (5 x+3))}{1331000} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)^2),x]

[Out]

(359370*(2 + 3*x) - (11*(900367 + 1500641*x))/(-3 + x + 10*x^2) + 2658250*Log[3
- 6*x] + 1088*Log[-3*(3 + 5*x)])/1331000

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Maple [A]  time = 0.014, size = 39, normalized size = 0.8 \[{\frac{81\,x}{100}}-{\frac{1}{45375+75625\,x}}+{\frac{136\,\ln \left ( 3+5\,x \right ) }{166375}}-{\frac{2401}{-968+1936\,x}}+{\frac{10633\,\ln \left ( -1+2\,x \right ) }{5324}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^4/(1-2*x)^2/(3+5*x)^2,x)

[Out]

81/100*x-1/15125/(3+5*x)+136/166375*ln(3+5*x)-2401/968/(-1+2*x)+10633/5324*ln(-1
+2*x)

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Maxima [A]  time = 1.35707, size = 50, normalized size = 1.04 \[ \frac{81}{100} \, x - \frac{1500641 \, x + 900367}{121000 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{136}{166375} \, \log \left (5 \, x + 3\right ) + \frac{10633}{5324} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^4/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="maxima")

[Out]

81/100*x - 1/121000*(1500641*x + 900367)/(10*x^2 + x - 3) + 136/166375*log(5*x +
3) + 10633/5324*log(2*x - 1)

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Fricas [A]  time = 0.21401, size = 80, normalized size = 1.67 \[ \frac{10781100 \, x^{3} + 1078110 \, x^{2} + 1088 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 2658250 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 19741381 \, x - 9904037}{1331000 \,{\left (10 \, x^{2} + x - 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^4/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="fricas")

[Out]

1/1331000*(10781100*x^3 + 1078110*x^2 + 1088*(10*x^2 + x - 3)*log(5*x + 3) + 265
8250*(10*x^2 + x - 3)*log(2*x - 1) - 19741381*x - 9904037)/(10*x^2 + x - 3)

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Sympy [A]  time = 0.387603, size = 39, normalized size = 0.81 \[ \frac{81 x}{100} - \frac{1500641 x + 900367}{1210000 x^{2} + 121000 x - 363000} + \frac{10633 \log{\left (x - \frac{1}{2} \right )}}{5324} + \frac{136 \log{\left (x + \frac{3}{5} \right )}}{166375} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**4/(1-2*x)**2/(3+5*x)**2,x)

[Out]

81*x/100 - (1500641*x + 900367)/(1210000*x**2 + 121000*x - 363000) + 10633*log(x
- 1/2)/5324 + 136*log(x + 3/5)/166375

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GIAC/XCAS [A]  time = 0.206504, size = 100, normalized size = 2.08 \[ \frac{{\left (5 \, x + 3\right )}{\left (\frac{1343273}{5 \, x + 3} - 107811\right )}}{332750 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{1}{15125 \,{\left (5 \, x + 3\right )}} - \frac{999}{500} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{10633}{5324} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^4/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="giac")

[Out]

1/332750*(5*x + 3)*(1343273/(5*x + 3) - 107811)/(11/(5*x + 3) - 2) - 1/15125/(5*
x + 3) - 999/500*ln(1/5*abs(5*x + 3)/(5*x + 3)^2) + 10633/5324*ln(abs(-11/(5*x +
3) + 2))