3.1477 \(\int \frac{1}{(1-2 x) (2+3 x) (3+5 x)} \, dx\)

Optimal. Leaf size=31 \[ -\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3) \]

[Out]

(-2*Log[1 - 2*x])/77 - (3*Log[2 + 3*x])/7 + (5*Log[3 + 5*x])/11

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Rubi [A]  time = 0.0451922, antiderivative size = 31, 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 \[ -\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(-2*Log[1 - 2*x])/77 - (3*Log[2 + 3*x])/7 + (5*Log[3 + 5*x])/11

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Rubi in Sympy [A]  time = 6.4793, size = 29, normalized size = 0.94 \[ - \frac{2 \log{\left (- 2 x + 1 \right )}}{77} - \frac{3 \log{\left (3 x + 2 \right )}}{7} + \frac{5 \log{\left (5 x + 3 \right )}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*log(-2*x + 1)/77 - 3*log(3*x + 2)/7 + 5*log(5*x + 3)/11

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Mathematica [A]  time = 0.0115671, size = 31, normalized size = 1. \[ -\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(-2*Log[1 - 2*x])/77 - (3*Log[2 + 3*x])/7 + (5*Log[3 + 5*x])/11

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Maple [A]  time = 0.01, size = 26, normalized size = 0.8 \[{\frac{5\,\ln \left ( 3+5\,x \right ) }{11}}-{\frac{3\,\ln \left ( 2+3\,x \right ) }{7}}-{\frac{2\,\ln \left ( -1+2\,x \right ) }{77}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/11*ln(3+5*x)-3/7*ln(2+3*x)-2/77*ln(-1+2*x)

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Maxima [A]  time = 1.33952, size = 34, normalized size = 1.1 \[ \frac{5}{11} \, \log \left (5 \, x + 3\right ) - \frac{3}{7} \, \log \left (3 \, x + 2\right ) - \frac{2}{77} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/11*log(5*x + 3) - 3/7*log(3*x + 2) - 2/77*log(2*x - 1)

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Fricas [A]  time = 0.216573, size = 34, normalized size = 1.1 \[ \frac{5}{11} \, \log \left (5 \, x + 3\right ) - \frac{3}{7} \, \log \left (3 \, x + 2\right ) - \frac{2}{77} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/11*log(5*x + 3) - 3/7*log(3*x + 2) - 2/77*log(2*x - 1)

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Sympy [A]  time = 0.308153, size = 29, normalized size = 0.94 \[ - \frac{2 \log{\left (x - \frac{1}{2} \right )}}{77} + \frac{5 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{3 \log{\left (x + \frac{2}{3} \right )}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*log(x - 1/2)/77 + 5*log(x + 3/5)/11 - 3*log(x + 2/3)/7

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GIAC/XCAS [A]  time = 0.209065, size = 38, normalized size = 1.23 \[ \frac{5}{11} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{3}{7} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{2}{77} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/11*ln(abs(5*x + 3)) - 3/7*ln(abs(3*x + 2)) - 2/77*ln(abs(2*x - 1))