3.1198 \(\int \frac{1-2 x}{(2+3 x) (3+5 x)^2} \, dx\)

Optimal. Leaf size=28 \[ -\frac{11}{5 (5 x+3)}+7 \log (3 x+2)-7 \log (5 x+3) \]

[Out]

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

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Rubi [A]  time = 0.0365849, antiderivative size = 28, 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 \[ -\frac{11}{5 (5 x+3)}+7 \log (3 x+2)-7 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

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

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Rubi in Sympy [A]  time = 5.71136, size = 22, normalized size = 0.79 \[ 7 \log{\left (3 x + 2 \right )} - 7 \log{\left (5 x + 3 \right )} - \frac{11}{5 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.0233044, size = 30, normalized size = 1.07 \[ -\frac{11}{5 (5 x+3)}+7 \log (5 (3 x+2))-7 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

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

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Maple [A]  time = 0.01, size = 27, normalized size = 1. \[ -{\frac{11}{15+25\,x}}+7\,\ln \left ( 2+3\,x \right ) -7\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Maxima [A]  time = 1.34007, size = 35, normalized size = 1.25 \[ -\frac{11}{5 \,{\left (5 \, x + 3\right )}} - 7 \, \log \left (5 \, x + 3\right ) + 7 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.209595, size = 50, normalized size = 1.79 \[ -\frac{35 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 35 \,{\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 11}{5 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/5*(35*(5*x + 3)*log(5*x + 3) - 35*(5*x + 3)*log(3*x + 2) + 11)/(5*x + 3)

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Sympy [A]  time = 0.240026, size = 22, normalized size = 0.79 \[ - 7 \log{\left (x + \frac{3}{5} \right )} + 7 \log{\left (x + \frac{2}{3} \right )} - \frac{11}{25 x + 15} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7*log(x + 3/5) + 7*log(x + 2/3) - 11/(25*x + 15)

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GIAC/XCAS [A]  time = 0.207719, size = 34, normalized size = 1.21 \[ -\frac{11}{5 \,{\left (5 \, x + 3\right )}} + 7 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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