3.1563 \(\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)} \, dx\)

Optimal. Leaf size=37 \[ \frac{125 x}{12}+\frac{1331}{56 (1-2 x)}+\frac{1089}{49} \log (1-2 x)-\frac{1}{441} \log (3 x+2) \]

[Out]

1331/(56*(1 - 2*x)) + (125*x)/12 + (1089*Log[1 - 2*x])/49 - Log[2 + 3*x]/441

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Rubi [A]  time = 0.045395, 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 \[ \frac{125 x}{12}+\frac{1331}{56 (1-2 x)}+\frac{1089}{49} \log (1-2 x)-\frac{1}{441} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

1331/(56*(1 - 2*x)) + (125*x)/12 + (1089*Log[1 - 2*x])/49 - Log[2 + 3*x]/441

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{1089 \log{\left (- 2 x + 1 \right )}}{49} - \frac{\log{\left (3 x + 2 \right )}}{441} + \int \frac{125}{12}\, dx + \frac{1331}{56 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1089*log(-2*x + 1)/49 - log(3*x + 2)/441 + Integral(125/12, x) + 1331/(56*(-2*x
+ 1))

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Mathematica [A]  time = 0.0401771, size = 37, normalized size = 1. \[ \frac{12250 (3 x+2)+\frac{83853}{1-2 x}+78408 \log (3-6 x)-8 \log (3 x+2)}{3528} \]

Antiderivative was successfully verified.

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

[Out]

(83853/(1 - 2*x) + 12250*(2 + 3*x) + 78408*Log[3 - 6*x] - 8*Log[2 + 3*x])/3528

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Maple [A]  time = 0.011, size = 30, normalized size = 0.8 \[{\frac{125\,x}{12}}-{\frac{\ln \left ( 2+3\,x \right ) }{441}}-{\frac{1331}{-56+112\,x}}+{\frac{1089\,\ln \left ( -1+2\,x \right ) }{49}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/12*x-1/441*ln(2+3*x)-1331/56/(-1+2*x)+1089/49*ln(-1+2*x)

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Maxima [A]  time = 1.35868, size = 39, normalized size = 1.05 \[ \frac{125}{12} \, x - \frac{1331}{56 \,{\left (2 \, x - 1\right )}} - \frac{1}{441} \, \log \left (3 \, x + 2\right ) + \frac{1089}{49} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/12*x - 1331/56/(2*x - 1) - 1/441*log(3*x + 2) + 1089/49*log(2*x - 1)

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Fricas [A]  time = 0.213624, size = 61, normalized size = 1.65 \[ \frac{73500 \, x^{2} - 8 \,{\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) + 78408 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 36750 \, x - 83853}{3528 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3528*(73500*x^2 - 8*(2*x - 1)*log(3*x + 2) + 78408*(2*x - 1)*log(2*x - 1) - 36
750*x - 83853)/(2*x - 1)

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Sympy [A]  time = 0.317975, size = 29, normalized size = 0.78 \[ \frac{125 x}{12} + \frac{1089 \log{\left (x - \frac{1}{2} \right )}}{49} - \frac{\log{\left (x + \frac{2}{3} \right )}}{441} - \frac{1331}{112 x - 56} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125*x/12 + 1089*log(x - 1/2)/49 - log(x + 2/3)/441 - 1331/(112*x - 56)

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GIAC/XCAS [A]  time = 0.205266, size = 63, normalized size = 1.7 \[ \frac{125}{12} \, x - \frac{1331}{56 \,{\left (2 \, x - 1\right )}} - \frac{200}{9} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) - \frac{1}{441} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) - \frac{125}{24} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/12*x - 1331/56/(2*x - 1) - 200/9*ln(1/2*abs(2*x - 1)/(2*x - 1)^2) - 1/441*ln
(abs(-7/(2*x - 1) - 3)) - 125/24