3.1544 \(\int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=34 \[ \frac{75 x^2}{8}+\frac{215 x}{4}+\frac{847}{16 (1-2 x)}+\frac{1133}{16} \log (1-2 x) \]

[Out]

847/(16*(1 - 2*x)) + (215*x)/4 + (75*x^2)/8 + (1133*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0457221, antiderivative size = 34, 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 \[ \frac{75 x^2}{8}+\frac{215 x}{4}+\frac{847}{16 (1-2 x)}+\frac{1133}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

847/(16*(1 - 2*x)) + (215*x)/4 + (75*x^2)/8 + (1133*Log[1 - 2*x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{1133 \log{\left (- 2 x + 1 \right )}}{16} + \int \frac{215}{4}\, dx + \frac{75 \int x\, dx}{4} + \frac{847}{16 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1133*log(-2*x + 1)/16 + Integral(215/4, x) + 75*Integral(x, x)/4 + 847/(16*(-2*x
+ 1))

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Mathematica [A]  time = 0.0170445, size = 36, normalized size = 1.06 \[ \frac{600 x^3+3140 x^2-3590 x+2266 (2 x-1) \log (1-2 x)-759}{64 x-32} \]

Antiderivative was successfully verified.

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

[Out]

(-759 - 3590*x + 3140*x^2 + 600*x^3 + 2266*(-1 + 2*x)*Log[1 - 2*x])/(-32 + 64*x)

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Maple [A]  time = 0.008, size = 27, normalized size = 0.8 \[{\frac{75\,{x}^{2}}{8}}+{\frac{215\,x}{4}}-{\frac{847}{-16+32\,x}}+{\frac{1133\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75/8*x^2+215/4*x-847/16/(-1+2*x)+1133/16*ln(-1+2*x)

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Maxima [A]  time = 1.35574, size = 35, normalized size = 1.03 \[ \frac{75}{8} \, x^{2} + \frac{215}{4} \, x - \frac{847}{16 \,{\left (2 \, x - 1\right )}} + \frac{1133}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75/8*x^2 + 215/4*x - 847/16/(2*x - 1) + 1133/16*log(2*x - 1)

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Fricas [A]  time = 0.199545, size = 50, normalized size = 1.47 \[ \frac{300 \, x^{3} + 1570 \, x^{2} + 1133 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 860 \, x - 847}{16 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/16*(300*x^3 + 1570*x^2 + 1133*(2*x - 1)*log(2*x - 1) - 860*x - 847)/(2*x - 1)

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Sympy [A]  time = 0.195006, size = 27, normalized size = 0.79 \[ \frac{75 x^{2}}{8} + \frac{215 x}{4} + \frac{1133 \log{\left (2 x - 1 \right )}}{16} - \frac{847}{32 x - 16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75*x**2/8 + 215*x/4 + 1133*log(2*x - 1)/16 - 847/(32*x - 16)

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GIAC/XCAS [A]  time = 0.220286, size = 65, normalized size = 1.91 \[ \frac{5}{32} \,{\left (2 \, x - 1\right )}^{2}{\left (\frac{202}{2 \, x - 1} + 15\right )} - \frac{847}{16 \,{\left (2 \, x - 1\right )}} - \frac{1133}{16} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/32*(2*x - 1)^2*(202/(2*x - 1) + 15) - 847/16/(2*x - 1) - 1133/16*ln(1/2*abs(2*
x - 1)/(2*x - 1)^2)