3.1622 \(\int \frac{3+5 x}{(1-2 x)^3 (2+3 x)} \, dx\)

Optimal. Leaf size=43 \[ -\frac{1}{49 (1-2 x)}+\frac{11}{28 (1-2 x)^2}+\frac{3}{343} \log (1-2 x)-\frac{3}{343} \log (3 x+2) \]

[Out]

11/(28*(1 - 2*x)^2) - 1/(49*(1 - 2*x)) + (3*Log[1 - 2*x])/343 - (3*Log[2 + 3*x])
/343

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Rubi [A]  time = 0.0473223, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{1}{49 (1-2 x)}+\frac{11}{28 (1-2 x)^2}+\frac{3}{343} \log (1-2 x)-\frac{3}{343} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

11/(28*(1 - 2*x)^2) - 1/(49*(1 - 2*x)) + (3*Log[1 - 2*x])/343 - (3*Log[2 + 3*x])
/343

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Rubi in Sympy [A]  time = 7.28612, size = 36, normalized size = 0.84 \[ \frac{3 \log{\left (- 2 x + 1 \right )}}{343} - \frac{3 \log{\left (3 x + 2 \right )}}{343} - \frac{1}{49 \left (- 2 x + 1\right )} + \frac{11}{28 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*log(-2*x + 1)/343 - 3*log(3*x + 2)/343 - 1/(49*(-2*x + 1)) + 11/(28*(-2*x + 1)
**2)

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Mathematica [A]  time = 0.0308796, size = 35, normalized size = 0.81 \[ \frac{\frac{7 (8 x+73)}{(1-2 x)^2}+12 \log (1-2 x)-12 \log (6 x+4)}{1372} \]

Antiderivative was successfully verified.

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

[Out]

((7*(73 + 8*x))/(1 - 2*x)^2 + 12*Log[1 - 2*x] - 12*Log[4 + 6*x])/1372

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Maple [A]  time = 0.012, size = 36, normalized size = 0.8 \[ -{\frac{3\,\ln \left ( 2+3\,x \right ) }{343}}+{\frac{11}{28\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{1}{-49+98\,x}}+{\frac{3\,\ln \left ( -1+2\,x \right ) }{343}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3/343*ln(2+3*x)+11/28/(-1+2*x)^2+1/49/(-1+2*x)+3/343*ln(-1+2*x)

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Maxima [A]  time = 1.32276, size = 49, normalized size = 1.14 \[ \frac{8 \, x + 73}{196 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{3}{343} \, \log \left (3 \, x + 2\right ) + \frac{3}{343} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/196*(8*x + 73)/(4*x^2 - 4*x + 1) - 3/343*log(3*x + 2) + 3/343*log(2*x - 1)

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Fricas [A]  time = 0.220092, size = 74, normalized size = 1.72 \[ -\frac{12 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 12 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 56 \, x - 511}{1372 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1372*(12*(4*x^2 - 4*x + 1)*log(3*x + 2) - 12*(4*x^2 - 4*x + 1)*log(2*x - 1) -
56*x - 511)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.324202, size = 34, normalized size = 0.79 \[ \frac{8 x + 73}{784 x^{2} - 784 x + 196} + \frac{3 \log{\left (x - \frac{1}{2} \right )}}{343} - \frac{3 \log{\left (x + \frac{2}{3} \right )}}{343} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(8*x + 73)/(784*x**2 - 784*x + 196) + 3*log(x - 1/2)/343 - 3*log(x + 2/3)/343

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GIAC/XCAS [A]  time = 0.206342, size = 45, normalized size = 1.05 \[ \frac{8 \, x + 73}{196 \,{\left (2 \, x - 1\right )}^{2}} - \frac{3}{343} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{3}{343} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/196*(8*x + 73)/(2*x - 1)^2 - 3/343*ln(abs(3*x + 2)) + 3/343*ln(abs(2*x - 1))