3.1476 \(\int \frac{1}{(1-2 x) (3+5 x)} \, dx\)

Optimal. Leaf size=21 \[ \frac{1}{11} \log (5 x+3)-\frac{1}{11} \log (1-2 x) \]

[Out]

-Log[1 - 2*x]/11 + Log[3 + 5*x]/11

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Rubi [A]  time = 0.0150082, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{1}{11} \log (5 x+3)-\frac{1}{11} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[1/((1 - 2*x)*(3 + 5*x)),x]

[Out]

-Log[1 - 2*x]/11 + Log[3 + 5*x]/11

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Rubi in Sympy [A]  time = 3.03505, size = 15, normalized size = 0.71 \[ - \frac{\log{\left (- 2 x + 1 \right )}}{11} + \frac{\log{\left (5 x + 3 \right )}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-log(-2*x + 1)/11 + log(5*x + 3)/11

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Mathematica [A]  time = 0.00558722, size = 21, normalized size = 1. \[ \frac{1}{11} \log (5 x+3)-\frac{1}{11} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

-Log[1 - 2*x]/11 + Log[3 + 5*x]/11

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Maple [A]  time = 0.007, size = 18, normalized size = 0.9 \[{\frac{\ln \left ( 3+5\,x \right ) }{11}}-{\frac{\ln \left ( -1+2\,x \right ) }{11}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1-2*x)/(3+5*x),x)

[Out]

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

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Maxima [A]  time = 1.34193, size = 23, normalized size = 1.1 \[ \frac{1}{11} \, \log \left (5 \, x + 3\right ) - \frac{1}{11} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/11*log(5*x + 3) - 1/11*log(2*x - 1)

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Fricas [A]  time = 0.214967, size = 23, normalized size = 1.1 \[ \frac{1}{11} \, \log \left (5 \, x + 3\right ) - \frac{1}{11} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/11*log(5*x + 3) - 1/11*log(2*x - 1)

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Sympy [A]  time = 0.193946, size = 15, normalized size = 0.71 \[ - \frac{\log{\left (x - \frac{1}{2} \right )}}{11} + \frac{\log{\left (x + \frac{3}{5} \right )}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(1-2*x)/(3+5*x),x)

[Out]

-log(x - 1/2)/11 + log(x + 3/5)/11

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GIAC/XCAS [A]  time = 0.206799, size = 26, normalized size = 1.24 \[ \frac{1}{11} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{1}{11} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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