3.1489 \(\int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)^2} \, dx\)

Optimal. Leaf size=37 \[ -\frac{27 x}{50}-\frac{1}{1375 (5 x+3)}-\frac{343}{484} \log (1-2 x)+\frac{101 \log (5 x+3)}{15125} \]

[Out]

(-27*x)/50 - 1/(1375*(3 + 5*x)) - (343*Log[1 - 2*x])/484 + (101*Log[3 + 5*x])/15
125

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Rubi [A]  time = 0.0463307, 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 \[ -\frac{27 x}{50}-\frac{1}{1375 (5 x+3)}-\frac{343}{484} \log (1-2 x)+\frac{101 \log (5 x+3)}{15125} \]

Antiderivative was successfully verified.

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

[Out]

(-27*x)/50 - 1/(1375*(3 + 5*x)) - (343*Log[1 - 2*x])/484 + (101*Log[3 + 5*x])/15
125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{343 \log{\left (- 2 x + 1 \right )}}{484} + \frac{101 \log{\left (5 x + 3 \right )}}{15125} + \int \left (- \frac{27}{50}\right )\, dx - \frac{1}{1375 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-343*log(-2*x + 1)/484 + 101*log(5*x + 3)/15125 + Integral(-27/50, x) - 1/(1375*
(5*x + 3))

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Mathematica [A]  time = 0.0336872, size = 37, normalized size = 1. \[ \frac{16335 (1-2 x)-\frac{44}{5 x+3}-42875 \log (1-2 x)+404 \log (10 x+6)}{60500} \]

Antiderivative was successfully verified.

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

[Out]

(16335*(1 - 2*x) - 44/(3 + 5*x) - 42875*Log[1 - 2*x] + 404*Log[6 + 10*x])/60500

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Maple [A]  time = 0.012, size = 30, normalized size = 0.8 \[ -{\frac{27\,x}{50}}-{\frac{1}{4125+6875\,x}}+{\frac{101\,\ln \left ( 3+5\,x \right ) }{15125}}-{\frac{343\,\ln \left ( -1+2\,x \right ) }{484}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/50*x-1/1375/(3+5*x)+101/15125*ln(3+5*x)-343/484*ln(-1+2*x)

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Maxima [A]  time = 1.33782, size = 39, normalized size = 1.05 \[ -\frac{27}{50} \, x - \frac{1}{1375 \,{\left (5 \, x + 3\right )}} + \frac{101}{15125} \, \log \left (5 \, x + 3\right ) - \frac{343}{484} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/50*x - 1/1375/(5*x + 3) + 101/15125*log(5*x + 3) - 343/484*log(2*x - 1)

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Fricas [A]  time = 0.226414, size = 61, normalized size = 1.65 \[ -\frac{163350 \, x^{2} - 404 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 42875 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 98010 \, x + 44}{60500 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/60500*(163350*x^2 - 404*(5*x + 3)*log(5*x + 3) + 42875*(5*x + 3)*log(2*x - 1)
+ 98010*x + 44)/(5*x + 3)

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Sympy [A]  time = 0.352373, size = 31, normalized size = 0.84 \[ - \frac{27 x}{50} - \frac{343 \log{\left (x - \frac{1}{2} \right )}}{484} + \frac{101 \log{\left (x + \frac{3}{5} \right )}}{15125} - \frac{1}{6875 x + 4125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27*x/50 - 343*log(x - 1/2)/484 + 101*log(x + 3/5)/15125 - 1/(6875*x + 4125)

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GIAC/XCAS [A]  time = 0.21269, size = 63, normalized size = 1.7 \[ -\frac{27}{50} \, x - \frac{1}{1375 \,{\left (5 \, x + 3\right )}} + \frac{351}{500} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{343}{484} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) - \frac{81}{250} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/50*x - 1/1375/(5*x + 3) + 351/500*ln(1/5*abs(5*x + 3)/(5*x + 3)^2) - 343/484
*ln(abs(-11/(5*x + 3) + 2)) - 81/250