3.1527 \(\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=32 \[ \frac{45 x^2}{8}+33 x+\frac{539}{16 (1-2 x)}+\frac{707}{16} \log (1-2 x) \]

[Out]

539/(16*(1 - 2*x)) + 33*x + (45*x^2)/8 + (707*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0452811, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{45 x^2}{8}+33 x+\frac{539}{16 (1-2 x)}+\frac{707}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

539/(16*(1 - 2*x)) + 33*x + (45*x^2)/8 + (707*Log[1 - 2*x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 33 x + \frac{707 \log{\left (- 2 x + 1 \right )}}{16} + \frac{45 \int x\, dx}{4} + \frac{539}{16 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

33*x + 707*log(-2*x + 1)/16 + 45*Integral(x, x)/4 + 539/(16*(-2*x + 1))

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Mathematica [A]  time = 0.0169281, size = 36, normalized size = 1.12 \[ \frac{360 x^3+1932 x^2-2202 x+1414 (2 x-1) \log (1-2 x)-505}{64 x-32} \]

Antiderivative was successfully verified.

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

[Out]

(-505 - 2202*x + 1932*x^2 + 360*x^3 + 1414*(-1 + 2*x)*Log[1 - 2*x])/(-32 + 64*x)

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Maple [A]  time = 0.01, size = 27, normalized size = 0.8 \[{\frac{45\,{x}^{2}}{8}}+33\,x-{\frac{539}{-16+32\,x}}+{\frac{707\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

45/8*x^2+33*x-539/16/(-1+2*x)+707/16*ln(-1+2*x)

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Maxima [A]  time = 1.34501, size = 35, normalized size = 1.09 \[ \frac{45}{8} \, x^{2} + 33 \, x - \frac{539}{16 \,{\left (2 \, x - 1\right )}} + \frac{707}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

45/8*x^2 + 33*x - 539/16/(2*x - 1) + 707/16*log(2*x - 1)

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Fricas [A]  time = 0.205345, size = 50, normalized size = 1.56 \[ \frac{180 \, x^{3} + 966 \, x^{2} + 707 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 528 \, x - 539}{16 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/16*(180*x^3 + 966*x^2 + 707*(2*x - 1)*log(2*x - 1) - 528*x - 539)/(2*x - 1)

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Sympy [A]  time = 0.196417, size = 26, normalized size = 0.81 \[ \frac{45 x^{2}}{8} + 33 x + \frac{707 \log{\left (2 x - 1 \right )}}{16} - \frac{539}{32 x - 16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

45*x**2/8 + 33*x + 707*log(2*x - 1)/16 - 539/(32*x - 16)

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GIAC/XCAS [A]  time = 0.20693, size = 65, normalized size = 2.03 \[ \frac{3}{32} \,{\left (2 \, x - 1\right )}^{2}{\left (\frac{206}{2 \, x - 1} + 15\right )} - \frac{539}{16 \,{\left (2 \, x - 1\right )}} - \frac{707}{16} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/32*(2*x - 1)^2*(206/(2*x - 1) + 15) - 539/16/(2*x - 1) - 707/16*ln(1/2*abs(2*x
- 1)/(2*x - 1)^2)