3.1524 \(\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=55 \[ \frac{243 x^5}{4}+\frac{2997 x^4}{8}+\frac{18027 x^3}{16}+\frac{75447 x^2}{32}+\frac{301467 x}{64}+\frac{184877}{128 (1-2 x)}+\frac{60025}{16} \log (1-2 x) \]

[Out]

184877/(128*(1 - 2*x)) + (301467*x)/64 + (75447*x^2)/32 + (18027*x^3)/16 + (2997
*x^4)/8 + (243*x^5)/4 + (60025*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0670924, antiderivative size = 55, 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 \[ \frac{243 x^5}{4}+\frac{2997 x^4}{8}+\frac{18027 x^3}{16}+\frac{75447 x^2}{32}+\frac{301467 x}{64}+\frac{184877}{128 (1-2 x)}+\frac{60025}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

184877/(128*(1 - 2*x)) + (301467*x)/64 + (75447*x^2)/32 + (18027*x^3)/16 + (2997
*x^4)/8 + (243*x^5)/4 + (60025*Log[1 - 2*x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{243 x^{5}}{4} + \frac{2997 x^{4}}{8} + \frac{18027 x^{3}}{16} + \frac{60025 \log{\left (- 2 x + 1 \right )}}{16} + \int \frac{301467}{64}\, dx + \frac{75447 \int x\, dx}{16} + \frac{184877}{128 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

243*x**5/4 + 2997*x**4/8 + 18027*x**3/16 + 60025*log(-2*x + 1)/16 + Integral(301
467/64, x) + 75447*Integral(x, x)/16 + 184877/(128*(-2*x + 1))

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Mathematica [A]  time = 0.0212456, size = 51, normalized size = 0.93 \[ \frac{1944 x^6+11016 x^5+30060 x^4+57420 x^3+113010 x^2-174912 x+60025 (2 x-1) \log (1-2 x)+26663}{32 x-16} \]

Antiderivative was successfully verified.

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

[Out]

(26663 - 174912*x + 113010*x^2 + 57420*x^3 + 30060*x^4 + 11016*x^5 + 1944*x^6 +
60025*(-1 + 2*x)*Log[1 - 2*x])/(-16 + 32*x)

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Maple [A]  time = 0.009, size = 42, normalized size = 0.8 \[{\frac{243\,{x}^{5}}{4}}+{\frac{2997\,{x}^{4}}{8}}+{\frac{18027\,{x}^{3}}{16}}+{\frac{75447\,{x}^{2}}{32}}+{\frac{301467\,x}{64}}-{\frac{184877}{-128+256\,x}}+{\frac{60025\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

243/4*x^5+2997/8*x^4+18027/16*x^3+75447/32*x^2+301467/64*x-184877/128/(-1+2*x)+6
0025/16*ln(-1+2*x)

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Maxima [A]  time = 1.34234, size = 55, normalized size = 1. \[ \frac{243}{4} \, x^{5} + \frac{2997}{8} \, x^{4} + \frac{18027}{16} \, x^{3} + \frac{75447}{32} \, x^{2} + \frac{301467}{64} \, x - \frac{184877}{128 \,{\left (2 \, x - 1\right )}} + \frac{60025}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

243/4*x^5 + 2997/8*x^4 + 18027/16*x^3 + 75447/32*x^2 + 301467/64*x - 184877/128/
(2*x - 1) + 60025/16*log(2*x - 1)

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Fricas [A]  time = 0.213424, size = 70, normalized size = 1.27 \[ \frac{15552 \, x^{6} + 88128 \, x^{5} + 240480 \, x^{4} + 459360 \, x^{3} + 904080 \, x^{2} + 480200 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 602934 \, x - 184877}{128 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/128*(15552*x^6 + 88128*x^5 + 240480*x^4 + 459360*x^3 + 904080*x^2 + 480200*(2*
x - 1)*log(2*x - 1) - 602934*x - 184877)/(2*x - 1)

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Sympy [A]  time = 0.228633, size = 48, normalized size = 0.87 \[ \frac{243 x^{5}}{4} + \frac{2997 x^{4}}{8} + \frac{18027 x^{3}}{16} + \frac{75447 x^{2}}{32} + \frac{301467 x}{64} + \frac{60025 \log{\left (2 x - 1 \right )}}{16} - \frac{184877}{256 x - 128} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

243*x**5/4 + 2997*x**4/8 + 18027*x**3/16 + 75447*x**2/32 + 301467*x/64 + 60025*l
og(2*x - 1)/16 - 184877/(256*x - 128)

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GIAC/XCAS [A]  time = 0.207105, size = 101, normalized size = 1.84 \[ \frac{3}{128} \,{\left (2 \, x - 1\right )}^{5}{\left (\frac{1404}{2 \, x - 1} + \frac{10815}{{\left (2 \, x - 1\right )}^{2}} + \frac{49980}{{\left (2 \, x - 1\right )}^{3}} + \frac{173215}{{\left (2 \, x - 1\right )}^{4}} + 81\right )} - \frac{184877}{128 \,{\left (2 \, x - 1\right )}} - \frac{60025}{16} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/128*(2*x - 1)^5*(1404/(2*x - 1) + 10815/(2*x - 1)^2 + 49980/(2*x - 1)^3 + 1732
15/(2*x - 1)^4 + 81) - 184877/128/(2*x - 1) - 60025/16*ln(1/2*abs(2*x - 1)/(2*x
- 1)^2)