3.1659 \(\int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)} \, dx\)

Optimal. Leaf size=43 \[ -\frac{392}{121 (1-2 x)}+\frac{343}{176 (1-2 x)^2}-\frac{7189 \log (1-2 x)}{10648}+\frac{\log (5 x+3)}{6655} \]

[Out]

343/(176*(1 - 2*x)^2) - 392/(121*(1 - 2*x)) - (7189*Log[1 - 2*x])/10648 + Log[3
+ 5*x]/6655

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Rubi [A]  time = 0.0502872, antiderivative size = 43, 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 \[ -\frac{392}{121 (1-2 x)}+\frac{343}{176 (1-2 x)^2}-\frac{7189 \log (1-2 x)}{10648}+\frac{\log (5 x+3)}{6655} \]

Antiderivative was successfully verified.

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

[Out]

343/(176*(1 - 2*x)^2) - 392/(121*(1 - 2*x)) - (7189*Log[1 - 2*x])/10648 + Log[3
+ 5*x]/6655

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Rubi in Sympy [A]  time = 7.81946, size = 34, normalized size = 0.79 \[ - \frac{7189 \log{\left (- 2 x + 1 \right )}}{10648} + \frac{\log{\left (5 x + 3 \right )}}{6655} - \frac{392}{121 \left (- 2 x + 1\right )} + \frac{343}{176 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7189*log(-2*x + 1)/10648 + log(5*x + 3)/6655 - 392/(121*(-2*x + 1)) + 343/(176*
(-2*x + 1)**2)

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Mathematica [A]  time = 0.0373977, size = 35, normalized size = 0.81 \[ \frac{\frac{2695 (256 x-51)}{(1-2 x)^2}-71890 \log (5-10 x)+16 \log (5 x+3)}{106480} \]

Antiderivative was successfully verified.

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

[Out]

((2695*(-51 + 256*x))/(1 - 2*x)^2 - 71890*Log[5 - 10*x] + 16*Log[3 + 5*x])/10648
0

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Maple [A]  time = 0.013, size = 36, normalized size = 0.8 \[{\frac{\ln \left ( 3+5\,x \right ) }{6655}}+{\frac{343}{176\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{392}{-121+242\,x}}-{\frac{7189\,\ln \left ( -1+2\,x \right ) }{10648}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6655*ln(3+5*x)+343/176/(-1+2*x)^2+392/121/(-1+2*x)-7189/10648*ln(-1+2*x)

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Maxima [A]  time = 1.35367, size = 49, normalized size = 1.14 \[ \frac{49 \,{\left (256 \, x - 51\right )}}{1936 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{6655} \, \log \left (5 \, x + 3\right ) - \frac{7189}{10648} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/1936*(256*x - 51)/(4*x^2 - 4*x + 1) + 1/6655*log(5*x + 3) - 7189/10648*log(2*
x - 1)

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Fricas [A]  time = 0.223764, size = 74, normalized size = 1.72 \[ \frac{16 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 71890 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 689920 \, x - 137445}{106480 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/106480*(16*(4*x^2 - 4*x + 1)*log(5*x + 3) - 71890*(4*x^2 - 4*x + 1)*log(2*x -
1) + 689920*x - 137445)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.402242, size = 32, normalized size = 0.74 \[ \frac{12544 x - 2499}{7744 x^{2} - 7744 x + 1936} - \frac{7189 \log{\left (x - \frac{1}{2} \right )}}{10648} + \frac{\log{\left (x + \frac{3}{5} \right )}}{6655} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(12544*x - 2499)/(7744*x**2 - 7744*x + 1936) - 7189*log(x - 1/2)/10648 + log(x +
3/5)/6655

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GIAC/XCAS [A]  time = 0.208246, size = 45, normalized size = 1.05 \[ \frac{49 \,{\left (256 \, x - 51\right )}}{1936 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{6655} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{7189}{10648} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/1936*(256*x - 51)/(2*x - 1)^2 + 1/6655*ln(abs(5*x + 3)) - 7189/10648*ln(abs(2
*x - 1))