3.1182 \(\int \frac{1-2 x}{3+5 x} \, dx\)

Optimal. Leaf size=16 \[ \frac{11}{25} \log (5 x+3)-\frac{2 x}{5} \]

[Out]

(-2*x)/5 + (11*Log[3 + 5*x])/25

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Rubi [A]  time = 0.0181853, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{11}{25} \log (5 x+3)-\frac{2 x}{5} \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)/(3 + 5*x),x]

[Out]

(-2*x)/5 + (11*Log[3 + 5*x])/25

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{11 \log{\left (5 x + 3 \right )}}{25} + \int \left (- \frac{2}{5}\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

11*log(5*x + 3)/25 + Integral(-2/5, x)

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Mathematica [A]  time = 0.00411722, size = 17, normalized size = 1.06 \[ \frac{1}{25} (-10 x+11 \log (5 x+3)-6) \]

Antiderivative was successfully verified.

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

[Out]

(-6 - 10*x + 11*Log[3 + 5*x])/25

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Maple [A]  time = 0.004, size = 13, normalized size = 0.8 \[ -{\frac{2\,x}{5}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{25}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)/(3+5*x),x)

[Out]

-2/5*x+11/25*ln(3+5*x)

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Maxima [A]  time = 1.34267, size = 16, normalized size = 1. \[ -\frac{2}{5} \, x + \frac{11}{25} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/5*x + 11/25*log(5*x + 3)

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Fricas [A]  time = 0.210205, size = 16, normalized size = 1. \[ -\frac{2}{5} \, x + \frac{11}{25} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/5*x + 11/25*log(5*x + 3)

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Sympy [A]  time = 0.115815, size = 14, normalized size = 0.88 \[ - \frac{2 x}{5} + \frac{11 \log{\left (5 x + 3 \right )}}{25} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)/(3+5*x),x)

[Out]

-2*x/5 + 11*log(5*x + 3)/25

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GIAC/XCAS [A]  time = 0.209821, size = 18, normalized size = 1.12 \[ -\frac{2}{5} \, x + \frac{11}{25} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/5*x + 11/25*ln(abs(5*x + 3))