3.1649 \(\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)} \, dx\)

Optimal. Leaf size=43 \[ -\frac{1089}{49 (1-2 x)}+\frac{1331}{112 (1-2 x)^2}-\frac{14289 \log (1-2 x)}{2744}-\frac{\log (3 x+2)}{1029} \]

[Out]

1331/(112*(1 - 2*x)^2) - 1089/(49*(1 - 2*x)) - (14289*Log[1 - 2*x])/2744 - Log[2
+ 3*x]/1029

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Rubi [A]  time = 0.0502588, 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 \[ -\frac{1089}{49 (1-2 x)}+\frac{1331}{112 (1-2 x)^2}-\frac{14289 \log (1-2 x)}{2744}-\frac{\log (3 x+2)}{1029} \]

Antiderivative was successfully verified.

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

[Out]

1331/(112*(1 - 2*x)^2) - 1089/(49*(1 - 2*x)) - (14289*Log[1 - 2*x])/2744 - Log[2
+ 3*x]/1029

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Rubi in Sympy [A]  time = 7.79384, size = 34, normalized size = 0.79 \[ - \frac{14289 \log{\left (- 2 x + 1 \right )}}{2744} - \frac{\log{\left (3 x + 2 \right )}}{1029} - \frac{1089}{49 \left (- 2 x + 1\right )} + \frac{1331}{112 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-14289*log(-2*x + 1)/2744 - log(3*x + 2)/1029 - 1089/(49*(-2*x + 1)) + 1331/(112
*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0389243, size = 35, normalized size = 0.81 \[ \frac{\frac{2541 (288 x-67)}{(1-2 x)^2}-85734 \log (3-6 x)-16 \log (3 x+2)}{16464} \]

Antiderivative was successfully verified.

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

[Out]

((2541*(-67 + 288*x))/(1 - 2*x)^2 - 85734*Log[3 - 6*x] - 16*Log[2 + 3*x])/16464

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Maple [A]  time = 0.01, size = 36, normalized size = 0.8 \[ -{\frac{\ln \left ( 2+3\,x \right ) }{1029}}+{\frac{1331}{112\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{1089}{-49+98\,x}}-{\frac{14289\,\ln \left ( -1+2\,x \right ) }{2744}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1029*ln(2+3*x)+1331/112/(-1+2*x)^2+1089/49/(-1+2*x)-14289/2744*ln(-1+2*x)

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Maxima [A]  time = 1.34674, size = 49, normalized size = 1.14 \[ \frac{121 \,{\left (288 \, x - 67\right )}}{784 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{1}{1029} \, \log \left (3 \, x + 2\right ) - \frac{14289}{2744} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121/784*(288*x - 67)/(4*x^2 - 4*x + 1) - 1/1029*log(3*x + 2) - 14289/2744*log(2*
x - 1)

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Fricas [A]  time = 0.219914, size = 74, normalized size = 1.72 \[ -\frac{16 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) + 85734 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 731808 \, x + 170247}{16464 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/16464*(16*(4*x^2 - 4*x + 1)*log(3*x + 2) + 85734*(4*x^2 - 4*x + 1)*log(2*x -
1) - 731808*x + 170247)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.423795, size = 32, normalized size = 0.74 \[ \frac{34848 x - 8107}{3136 x^{2} - 3136 x + 784} - \frac{14289 \log{\left (x - \frac{1}{2} \right )}}{2744} - \frac{\log{\left (x + \frac{2}{3} \right )}}{1029} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(34848*x - 8107)/(3136*x**2 - 3136*x + 784) - 14289*log(x - 1/2)/2744 - log(x +
2/3)/1029

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GIAC/XCAS [A]  time = 0.21185, size = 45, normalized size = 1.05 \[ \frac{121 \,{\left (288 \, x - 67\right )}}{784 \,{\left (2 \, x - 1\right )}^{2}} - \frac{1}{1029} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{14289}{2744} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121/784*(288*x - 67)/(2*x - 1)^2 - 1/1029*ln(abs(3*x + 2)) - 14289/2744*ln(abs(2
*x - 1))