3.1579 \(\int \frac{1}{(1-2 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=32 \[ \frac{1}{11 (1-2 x)}-\frac{5}{121} \log (1-2 x)+\frac{5}{121} \log (5 x+3) \]

[Out]

1/(11*(1 - 2*x)) - (5*Log[1 - 2*x])/121 + (5*Log[3 + 5*x])/121

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Rubi [A]  time = 0.0291063, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{1}{11 (1-2 x)}-\frac{5}{121} \log (1-2 x)+\frac{5}{121} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

1/(11*(1 - 2*x)) - (5*Log[1 - 2*x])/121 + (5*Log[3 + 5*x])/121

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Rubi in Sympy [A]  time = 5.23839, size = 26, normalized size = 0.81 \[ - \frac{5 \log{\left (- 2 x + 1 \right )}}{121} + \frac{5 \log{\left (5 x + 3 \right )}}{121} + \frac{1}{11 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5*log(-2*x + 1)/121 + 5*log(5*x + 3)/121 + 1/(11*(-2*x + 1))

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Mathematica [A]  time = 0.0154968, size = 38, normalized size = 1.19 \[ \frac{(5-10 x) \log (1-2 x)+5 (2 x-1) \log (10 x+6)-11}{121 (2 x-1)} \]

Antiderivative was successfully verified.

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

[Out]

(-11 + (5 - 10*x)*Log[1 - 2*x] + 5*(-1 + 2*x)*Log[6 + 10*x])/(121*(-1 + 2*x))

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Maple [A]  time = 0.011, size = 27, normalized size = 0.8 \[{\frac{5\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{1}{-11+22\,x}}-{\frac{5\,\ln \left ( -1+2\,x \right ) }{121}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1-2*x)^2/(3+5*x),x)

[Out]

5/121*ln(3+5*x)-1/11/(-1+2*x)-5/121*ln(-1+2*x)

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Maxima [A]  time = 1.32244, size = 35, normalized size = 1.09 \[ -\frac{1}{11 \,{\left (2 \, x - 1\right )}} + \frac{5}{121} \, \log \left (5 \, x + 3\right ) - \frac{5}{121} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/11/(2*x - 1) + 5/121*log(5*x + 3) - 5/121*log(2*x - 1)

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Fricas [A]  time = 0.218131, size = 50, normalized size = 1.56 \[ \frac{5 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) - 5 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 11}{121 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/121*(5*(2*x - 1)*log(5*x + 3) - 5*(2*x - 1)*log(2*x - 1) - 11)/(2*x - 1)

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Sympy [A]  time = 0.262597, size = 26, normalized size = 0.81 \[ - \frac{5 \log{\left (x - \frac{1}{2} \right )}}{121} + \frac{5 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{1}{22 x - 11} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5*log(x - 1/2)/121 + 5*log(x + 3/5)/121 - 1/(22*x - 11)

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GIAC/XCAS [A]  time = 0.212463, size = 34, normalized size = 1.06 \[ -\frac{1}{11 \,{\left (2 \, x - 1\right )}} + \frac{5}{121} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/11/(2*x - 1) + 5/121*ln(abs(-11/(2*x - 1) - 5))