3.1576 \(\int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=37 \[ \frac{27 x}{20}+\frac{343}{88 (1-2 x)}+\frac{392}{121} \log (1-2 x)+\frac{\log (5 x+3)}{3025} \]

[Out]

343/(88*(1 - 2*x)) + (27*x)/20 + (392*Log[1 - 2*x])/121 + Log[3 + 5*x]/3025

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Rubi [A]  time = 0.0455784, antiderivative size = 37, 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 \[ \frac{27 x}{20}+\frac{343}{88 (1-2 x)}+\frac{392}{121} \log (1-2 x)+\frac{\log (5 x+3)}{3025} \]

Antiderivative was successfully verified.

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

[Out]

343/(88*(1 - 2*x)) + (27*x)/20 + (392*Log[1 - 2*x])/121 + Log[3 + 5*x]/3025

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{392 \log{\left (- 2 x + 1 \right )}}{121} + \frac{\log{\left (5 x + 3 \right )}}{3025} + \int \frac{27}{20}\, dx + \frac{343}{88 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

392*log(-2*x + 1)/121 + log(5*x + 3)/3025 + Integral(27/20, x) + 343/(88*(-2*x +
1))

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Mathematica [A]  time = 0.0369814, size = 37, normalized size = 1. \[ \frac{6534 (5 x+3)+\frac{94325}{1-2 x}+78400 \log (5-10 x)+8 \log (5 x+3)}{24200} \]

Antiderivative was successfully verified.

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

[Out]

(94325/(1 - 2*x) + 6534*(3 + 5*x) + 78400*Log[5 - 10*x] + 8*Log[3 + 5*x])/24200

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Maple [A]  time = 0.012, size = 30, normalized size = 0.8 \[{\frac{27\,x}{20}}+{\frac{\ln \left ( 3+5\,x \right ) }{3025}}-{\frac{343}{-88+176\,x}}+{\frac{392\,\ln \left ( -1+2\,x \right ) }{121}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

27/20*x+1/3025*ln(3+5*x)-343/88/(-1+2*x)+392/121*ln(-1+2*x)

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Maxima [A]  time = 1.34353, size = 39, normalized size = 1.05 \[ \frac{27}{20} \, x - \frac{343}{88 \,{\left (2 \, x - 1\right )}} + \frac{1}{3025} \, \log \left (5 \, x + 3\right ) + \frac{392}{121} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

27/20*x - 343/88/(2*x - 1) + 1/3025*log(5*x + 3) + 392/121*log(2*x - 1)

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Fricas [A]  time = 0.21406, size = 61, normalized size = 1.65 \[ \frac{65340 \, x^{2} + 8 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 78400 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 32670 \, x - 94325}{24200 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/24200*(65340*x^2 + 8*(2*x - 1)*log(5*x + 3) + 78400*(2*x - 1)*log(2*x - 1) - 3
2670*x - 94325)/(2*x - 1)

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Sympy [A]  time = 0.313586, size = 29, normalized size = 0.78 \[ \frac{27 x}{20} + \frac{392 \log{\left (x - \frac{1}{2} \right )}}{121} + \frac{\log{\left (x + \frac{3}{5} \right )}}{3025} - \frac{343}{176 x - 88} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

27*x/20 + 392*log(x - 1/2)/121 + log(x + 3/5)/3025 - 343/(176*x - 88)

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GIAC/XCAS [A]  time = 0.206926, size = 63, normalized size = 1.7 \[ \frac{27}{20} \, x - \frac{343}{88 \,{\left (2 \, x - 1\right )}} - \frac{81}{25} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{3025} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) - \frac{27}{40} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

27/20*x - 343/88/(2*x - 1) - 81/25*ln(1/2*abs(2*x - 1)/(2*x - 1)^2) + 1/3025*ln(
abs(-11/(2*x - 1) - 5)) - 27/40