3.1545 \(\int \frac{(3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=27 \[ \frac{25 x}{4}+\frac{121}{8 (1-2 x)}+\frac{55}{4} \log (1-2 x) \]

[Out]

121/(8*(1 - 2*x)) + (25*x)/4 + (55*Log[1 - 2*x])/4

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Rubi [A]  time = 0.0285156, 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 \[ \frac{25 x}{4}+\frac{121}{8 (1-2 x)}+\frac{55}{4} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^2/(1 - 2*x)^2,x]

[Out]

121/(8*(1 - 2*x)) + (25*x)/4 + (55*Log[1 - 2*x])/4

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{55 \log{\left (- 2 x + 1 \right )}}{4} + \int \frac{25}{4}\, dx + \frac{121}{8 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

55*log(-2*x + 1)/4 + Integral(25/4, x) + 121/(8*(-2*x + 1))

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Mathematica [A]  time = 0.018832, size = 26, normalized size = 0.96 \[ \frac{1}{8} \left (50 x+\frac{121}{1-2 x}+110 \log (1-2 x)-25\right ) \]

Antiderivative was successfully verified.

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

[Out]

(-25 + 121/(1 - 2*x) + 50*x + 110*Log[1 - 2*x])/8

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Maple [A]  time = 0.007, size = 22, normalized size = 0.8 \[{\frac{25\,x}{4}}-{\frac{121}{-8+16\,x}}+{\frac{55\,\ln \left ( -1+2\,x \right ) }{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^2/(1-2*x)^2,x)

[Out]

25/4*x-121/8/(-1+2*x)+55/4*ln(-1+2*x)

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Maxima [A]  time = 1.32071, size = 28, normalized size = 1.04 \[ \frac{25}{4} \, x - \frac{121}{8 \,{\left (2 \, x - 1\right )}} + \frac{55}{4} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25/4*x - 121/8/(2*x - 1) + 55/4*log(2*x - 1)

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Fricas [A]  time = 0.200907, size = 43, normalized size = 1.59 \[ \frac{100 \, x^{2} + 110 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 50 \, x - 121}{8 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8*(100*x^2 + 110*(2*x - 1)*log(2*x - 1) - 50*x - 121)/(2*x - 1)

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Sympy [A]  time = 0.169492, size = 20, normalized size = 0.74 \[ \frac{25 x}{4} + \frac{55 \log{\left (2 x - 1 \right )}}{4} - \frac{121}{16 x - 8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25*x/4 + 55*log(2*x - 1)/4 - 121/(16*x - 8)

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GIAC/XCAS [A]  time = 0.209945, size = 43, normalized size = 1.59 \[ \frac{25}{4} \, x - \frac{121}{8 \,{\left (2 \, x - 1\right )}} - \frac{55}{4} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) - \frac{25}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25/4*x - 121/8/(2*x - 1) - 55/4*ln(1/2*abs(2*x - 1)/(2*x - 1)^2) - 25/8