3.1295 \(\int \frac{(1-2 x)^2}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=27 \[ \frac{4 x}{25}-\frac{121}{125 (5 x+3)}-\frac{44}{125} \log (5 x+3) \]

[Out]

(4*x)/25 - 121/(125*(3 + 5*x)) - (44*Log[3 + 5*x])/125

_______________________________________________________________________________________

Rubi [A]  time = 0.0257625, antiderivative size = 27, 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 \[ \frac{4 x}{25}-\frac{121}{125 (5 x+3)}-\frac{44}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2/(3 + 5*x)^2,x]

[Out]

(4*x)/25 - 121/(125*(3 + 5*x)) - (44*Log[3 + 5*x])/125

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{44 \log{\left (5 x + 3 \right )}}{125} + \int \frac{4}{25}\, dx - \frac{121}{125 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-44*log(5*x + 3)/125 + Integral(4/25, x) - 121/(125*(5*x + 3))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0161537, size = 34, normalized size = 1.26 \[ \frac{100 x^2+10 x-44 (5 x+3) \log (10 x+6)-151}{125 (5 x+3)} \]

Antiderivative was successfully verified.

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

[Out]

(-151 + 10*x + 100*x^2 - 44*(3 + 5*x)*Log[6 + 10*x])/(125*(3 + 5*x))

_______________________________________________________________________________________

Maple [A]  time = 0.007, size = 22, normalized size = 0.8 \[{\frac{4\,x}{25}}-{\frac{121}{375+625\,x}}-{\frac{44\,\ln \left ( 3+5\,x \right ) }{125}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2/(3+5*x)^2,x)

[Out]

4/25*x-121/125/(3+5*x)-44/125*ln(3+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.33502, size = 28, normalized size = 1.04 \[ \frac{4}{25} \, x - \frac{121}{125 \,{\left (5 \, x + 3\right )}} - \frac{44}{125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/25*x - 121/125/(5*x + 3) - 44/125*log(5*x + 3)

_______________________________________________________________________________________

Fricas [A]  time = 0.206866, size = 43, normalized size = 1.59 \[ \frac{100 \, x^{2} - 44 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 60 \, x - 121}{125 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/125*(100*x^2 - 44*(5*x + 3)*log(5*x + 3) + 60*x - 121)/(5*x + 3)

_______________________________________________________________________________________

Sympy [A]  time = 0.186128, size = 20, normalized size = 0.74 \[ \frac{4 x}{25} - \frac{44 \log{\left (5 x + 3 \right )}}{125} - \frac{121}{625 x + 375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4*x/25 - 44*log(5*x + 3)/125 - 121/(625*x + 375)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.233796, size = 43, normalized size = 1.59 \[ \frac{4}{25} \, x - \frac{121}{125 \,{\left (5 \, x + 3\right )}} + \frac{44}{125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{12}{125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/25*x - 121/125/(5*x + 3) + 44/125*ln(1/5*abs(5*x + 3)/(5*x + 3)^2) + 12/125