3.1197 \(\int \frac{1-2 x}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=22 \[ -\frac{11}{25 (5 x+3)}-\frac{2}{25} \log (5 x+3) \]

[Out]

-11/(25*(3 + 5*x)) - (2*Log[3 + 5*x])/25

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Rubi [A]  time = 0.0209195, antiderivative size = 22, 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 \[ -\frac{11}{25 (5 x+3)}-\frac{2}{25} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)/(3 + 5*x)^2,x]

[Out]

-11/(25*(3 + 5*x)) - (2*Log[3 + 5*x])/25

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Rubi in Sympy [A]  time = 3.98075, size = 17, normalized size = 0.77 \[ - \frac{2 \log{\left (5 x + 3 \right )}}{25} - \frac{11}{25 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00664381, size = 22, normalized size = 1. \[ -\frac{11}{25 (5 x+3)}-\frac{2}{25} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-11/(25*(3 + 5*x)) - (2*Log[3 + 5*x])/25

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Maple [A]  time = 0.007, size = 19, normalized size = 0.9 \[ -{\frac{11}{75+125\,x}}-{\frac{2\,\ln \left ( 3+5\,x \right ) }{25}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)/(3+5*x)^2,x)

[Out]

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

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Maxima [A]  time = 1.34224, size = 24, normalized size = 1.09 \[ -\frac{11}{25 \,{\left (5 \, x + 3\right )}} - \frac{2}{25} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11/25/(5*x + 3) - 2/25*log(5*x + 3)

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Fricas [A]  time = 0.213323, size = 32, normalized size = 1.45 \[ -\frac{2 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 11}{25 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/25*(2*(5*x + 3)*log(5*x + 3) + 11)/(5*x + 3)

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Sympy [A]  time = 0.162658, size = 17, normalized size = 0.77 \[ - \frac{2 \log{\left (5 x + 3 \right )}}{25} - \frac{11}{125 x + 75} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)/(3+5*x)**2,x)

[Out]

-2*log(5*x + 3)/25 - 11/(125*x + 75)

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GIAC/XCAS [A]  time = 0.209502, size = 38, normalized size = 1.73 \[ -\frac{11}{25 \,{\left (5 \, x + 3\right )}} + \frac{2}{25} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11/25/(5*x + 3) + 2/25*ln(1/5*abs(5*x + 3)/(5*x + 3)^2)