3.1423 \(\int \frac{(2+3 x)^2 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=30 \[ -\frac{15 x^3}{2}-\frac{219 x^2}{8}-\frac{443 x}{8}-\frac{539}{16} \log (1-2 x) \]

[Out]

(-443*x)/8 - (219*x^2)/8 - (15*x^3)/2 - (539*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0313721, antiderivative size = 30, 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 \[ -\frac{15 x^3}{2}-\frac{219 x^2}{8}-\frac{443 x}{8}-\frac{539}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-443*x)/8 - (219*x^2)/8 - (15*x^3)/2 - (539*Log[1 - 2*x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{15 x^{3}}{2} - \frac{539 \log{\left (- 2 x + 1 \right )}}{16} + \int \left (- \frac{443}{8}\right )\, dx - \frac{219 \int x\, dx}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*x**3/2 - 539*log(-2*x + 1)/16 + Integral(-443/8, x) - 219*Integral(x, x)/4

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Mathematica [A]  time = 0.0155329, size = 27, normalized size = 0.9 \[ \frac{1}{32} \left (-240 x^3-876 x^2-1772 x-1078 \log (1-2 x)+1135\right ) \]

Antiderivative was successfully verified.

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

[Out]

(1135 - 1772*x - 876*x^2 - 240*x^3 - 1078*Log[1 - 2*x])/32

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Maple [A]  time = 0.005, size = 23, normalized size = 0.8 \[ -{\frac{15\,{x}^{3}}{2}}-{\frac{219\,{x}^{2}}{8}}-{\frac{443\,x}{8}}-{\frac{539\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/2*x^3-219/8*x^2-443/8*x-539/16*ln(-1+2*x)

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Maxima [A]  time = 1.34886, size = 30, normalized size = 1. \[ -\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/2*x^3 - 219/8*x^2 - 443/8*x - 539/16*log(2*x - 1)

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Fricas [A]  time = 0.207288, size = 30, normalized size = 1. \[ -\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/2*x^3 - 219/8*x^2 - 443/8*x - 539/16*log(2*x - 1)

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Sympy [A]  time = 0.162866, size = 29, normalized size = 0.97 \[ - \frac{15 x^{3}}{2} - \frac{219 x^{2}}{8} - \frac{443 x}{8} - \frac{539 \log{\left (2 x - 1 \right )}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*x**3/2 - 219*x**2/8 - 443*x/8 - 539*log(2*x - 1)/16

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GIAC/XCAS [A]  time = 0.217479, size = 31, normalized size = 1.03 \[ -\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{16} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/2*x^3 - 219/8*x^2 - 443/8*x - 539/16*ln(abs(2*x - 1))