3.1183 \(\int \frac{1-2 x}{(2+3 x) (3+5 x)} \, dx\)

Optimal. Leaf size=21 \[ \frac{11}{5} \log (5 x+3)-\frac{7}{3} \log (3 x+2) \]

[Out]

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

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Rubi [A]  time = 0.0289911, 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 \[ \frac{11}{5} \log (5 x+3)-\frac{7}{3} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

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

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Rubi in Sympy [A]  time = 4.76688, size = 19, normalized size = 0.9 \[ - \frac{7 \log{\left (3 x + 2 \right )}}{3} + \frac{11 \log{\left (5 x + 3 \right )}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7*log(3*x + 2)/3 + 11*log(5*x + 3)/5

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Mathematica [A]  time = 0.00861362, size = 21, normalized size = 1. \[ \frac{11}{5} \log (5 x+3)-\frac{7}{3} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

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

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Maple [A]  time = 0.007, size = 18, normalized size = 0.9 \[ -{\frac{7\,\ln \left ( 2+3\,x \right ) }{3}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)/(2+3*x)/(3+5*x),x)

[Out]

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

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Maxima [A]  time = 1.3437, size = 23, normalized size = 1.1 \[ \frac{11}{5} \, \log \left (5 \, x + 3\right ) - \frac{7}{3} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

11/5*log(5*x + 3) - 7/3*log(3*x + 2)

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Fricas [A]  time = 0.223582, size = 23, normalized size = 1.1 \[ \frac{11}{5} \, \log \left (5 \, x + 3\right ) - \frac{7}{3} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

11/5*log(5*x + 3) - 7/3*log(3*x + 2)

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Sympy [A]  time = 0.218622, size = 19, normalized size = 0.9 \[ \frac{11 \log{\left (x + \frac{3}{5} \right )}}{5} - \frac{7 \log{\left (x + \frac{2}{3} \right )}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

11*log(x + 3/5)/5 - 7*log(x + 2/3)/3

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GIAC/XCAS [A]  time = 0.206424, size = 26, normalized size = 1.24 \[ \frac{11}{5} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{7}{3} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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