3.1424 \(\int \frac{(2+3 x) (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=23 \[ -\frac{15 x^2}{4}-\frac{53 x}{4}-\frac{77}{8} \log (1-2 x) \]

[Out]

(-53*x)/4 - (15*x^2)/4 - (77*Log[1 - 2*x])/8

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Rubi [A]  time = 0.0258681, antiderivative size = 23, 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 \[ -\frac{15 x^2}{4}-\frac{53 x}{4}-\frac{77}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-53*x)/4 - (15*x^2)/4 - (77*Log[1 - 2*x])/8

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{77 \log{\left (- 2 x + 1 \right )}}{8} + \int \left (- \frac{53}{4}\right )\, dx - \frac{15 \int x\, dx}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-77*log(-2*x + 1)/8 + Integral(-53/4, x) - 15*Integral(x, x)/2

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Mathematica [A]  time = 0.0074668, size = 22, normalized size = 0.96 \[ \frac{1}{16} \left (-60 x^2-212 x-154 \log (1-2 x)+121\right ) \]

Antiderivative was successfully verified.

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

[Out]

(121 - 212*x - 60*x^2 - 154*Log[1 - 2*x])/16

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Maple [A]  time = 0.003, size = 18, normalized size = 0.8 \[ -{\frac{15\,{x}^{2}}{4}}-{\frac{53\,x}{4}}-{\frac{77\,\ln \left ( -1+2\,x \right ) }{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)*(3+5*x)/(1-2*x),x)

[Out]

-15/4*x^2-53/4*x-77/8*ln(-1+2*x)

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Maxima [A]  time = 1.34167, size = 23, normalized size = 1. \[ -\frac{15}{4} \, x^{2} - \frac{53}{4} \, x - \frac{77}{8} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/4*x^2 - 53/4*x - 77/8*log(2*x - 1)

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Fricas [A]  time = 0.20743, size = 23, normalized size = 1. \[ -\frac{15}{4} \, x^{2} - \frac{53}{4} \, x - \frac{77}{8} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/4*x^2 - 53/4*x - 77/8*log(2*x - 1)

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Sympy [A]  time = 0.175364, size = 22, normalized size = 0.96 \[ - \frac{15 x^{2}}{4} - \frac{53 x}{4} - \frac{77 \log{\left (2 x - 1 \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*x**2/4 - 53*x/4 - 77*log(2*x - 1)/8

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GIAC/XCAS [A]  time = 0.218505, size = 24, normalized size = 1.04 \[ -\frac{15}{4} \, x^{2} - \frac{53}{4} \, x - \frac{77}{8} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/4*x^2 - 53/4*x - 77/8*ln(abs(2*x - 1))