3.1426 \(\int \frac{3+5 x}{(1-2 x) (2+3 x)} \, dx\)

Optimal. Leaf size=21 \[ -\frac{11}{14} \log (1-2 x)-\frac{1}{21} \log (3 x+2) \]

[Out]

(-11*Log[1 - 2*x])/14 - Log[2 + 3*x]/21

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Rubi [A]  time = 0.030089, antiderivative size = 21, 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 \[ -\frac{11}{14} \log (1-2 x)-\frac{1}{21} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(-11*Log[1 - 2*x])/14 - Log[2 + 3*x]/21

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Rubi in Sympy [A]  time = 5.37104, size = 19, normalized size = 0.9 \[ - \frac{11 \log{\left (- 2 x + 1 \right )}}{14} - \frac{\log{\left (3 x + 2 \right )}}{21} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11*log(-2*x + 1)/14 - log(3*x + 2)/21

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Mathematica [A]  time = 0.00746328, size = 21, normalized size = 1. \[ -\frac{11}{14} \log (1-2 x)-\frac{1}{21} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(-11*Log[1 - 2*x])/14 - Log[2 + 3*x]/21

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Maple [A]  time = 0.007, size = 18, normalized size = 0.9 \[ -{\frac{\ln \left ( 2+3\,x \right ) }{21}}-{\frac{11\,\ln \left ( -1+2\,x \right ) }{14}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)/(1-2*x)/(2+3*x),x)

[Out]

-1/21*ln(2+3*x)-11/14*ln(-1+2*x)

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Maxima [A]  time = 1.34493, size = 23, normalized size = 1.1 \[ -\frac{1}{21} \, \log \left (3 \, x + 2\right ) - \frac{11}{14} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*log(3*x + 2) - 11/14*log(2*x - 1)

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Fricas [A]  time = 0.216377, size = 23, normalized size = 1.1 \[ -\frac{1}{21} \, \log \left (3 \, x + 2\right ) - \frac{11}{14} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*log(3*x + 2) - 11/14*log(2*x - 1)

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Sympy [A]  time = 0.228797, size = 19, normalized size = 0.9 \[ - \frac{11 \log{\left (x - \frac{1}{2} \right )}}{14} - \frac{\log{\left (x + \frac{2}{3} \right )}}{21} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11*log(x - 1/2)/14 - log(x + 2/3)/21

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GIAC/XCAS [A]  time = 0.207204, size = 26, normalized size = 1.24 \[ -\frac{1}{21} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{11}{14} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*ln(abs(3*x + 2)) - 11/14*ln(abs(2*x - 1))