3.1528 \(\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=27 \[ \frac{15 x}{4}+\frac{77}{8 (1-2 x)}+\frac{17}{2} \log (1-2 x) \]

[Out]

77/(8*(1 - 2*x)) + (15*x)/4 + (17*Log[1 - 2*x])/2

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Rubi [A]  time = 0.0350932, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{15 x}{4}+\frac{77}{8 (1-2 x)}+\frac{17}{2} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

77/(8*(1 - 2*x)) + (15*x)/4 + (17*Log[1 - 2*x])/2

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{17 \log{\left (- 2 x + 1 \right )}}{2} + \int \frac{15}{4}\, dx + \frac{77}{8 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

17*log(-2*x + 1)/2 + Integral(15/4, x) + 77/(8*(-2*x + 1))

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Mathematica [A]  time = 0.0174186, size = 26, normalized size = 0.96 \[ \frac{1}{8} \left (30 x+\frac{77}{1-2 x}+68 \log (1-2 x)-15\right ) \]

Antiderivative was successfully verified.

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

[Out]

(-15 + 77/(1 - 2*x) + 30*x + 68*Log[1 - 2*x])/8

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Maple [A]  time = 0.008, size = 22, normalized size = 0.8 \[{\frac{15\,x}{4}}-{\frac{77}{-8+16\,x}}+{\frac{17\,\ln \left ( -1+2\,x \right ) }{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

15/4*x-77/8/(-1+2*x)+17/2*ln(-1+2*x)

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Maxima [A]  time = 1.36657, size = 28, normalized size = 1.04 \[ \frac{15}{4} \, x - \frac{77}{8 \,{\left (2 \, x - 1\right )}} + \frac{17}{2} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

15/4*x - 77/8/(2*x - 1) + 17/2*log(2*x - 1)

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Fricas [A]  time = 0.199296, size = 43, normalized size = 1.59 \[ \frac{60 \, x^{2} + 68 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 30 \, x - 77}{8 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8*(60*x^2 + 68*(2*x - 1)*log(2*x - 1) - 30*x - 77)/(2*x - 1)

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Sympy [A]  time = 0.169078, size = 20, normalized size = 0.74 \[ \frac{15 x}{4} + \frac{17 \log{\left (2 x - 1 \right )}}{2} - \frac{77}{16 x - 8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

15*x/4 + 17*log(2*x - 1)/2 - 77/(16*x - 8)

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GIAC/XCAS [A]  time = 0.207138, size = 43, normalized size = 1.59 \[ \frac{15}{4} \, x - \frac{77}{8 \,{\left (2 \, x - 1\right )}} - \frac{17}{2} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) - \frac{15}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

15/4*x - 77/8/(2*x - 1) - 17/2*ln(1/2*abs(2*x - 1)/(2*x - 1)^2) - 15/8