3.1541 \(\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^2} \, dx\)

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 = 0.027146, 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, Rules used = {77} \[ \frac{243 x^5}{4}+\frac{2997 x^4}{8}+\frac{18027 x^3}{16}+\frac{75447 x^2}{32}+\frac{301467 x}{64}+\frac{184877}{128 (1-2 x)}+\frac{60025}{16} \log (1-2 x) \]

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

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac{301467}{64}+\frac{75447 x}{16}+\frac{54081 x^2}{16}+\frac{2997 x^3}{2}+\frac{1215 x^4}{4}+\frac{184877}{64 (-1+2 x)^2}+\frac{60025}{8 (-1+2 x)}\right ) \, dx\\ &=\frac{184877}{128 (1-2 x)}+\frac{301467 x}{64}+\frac{75447 x^2}{32}+\frac{18027 x^3}{16}+\frac{2997 x^4}{8}+\frac{243 x^5}{4}+\frac{60025}{16} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0119141, 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 = 0.005, size = 42, normalized size = 0.8 \begin{align*}{\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\,\ln \left ( 2\,x-1 \right ) }{16}}-{\frac{184877}{256\,x-128}} \end{align*}

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+60025/16*ln(2*x-1)-184877/128/(2*x-1)

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Maxima [A]  time = 1.04697, size = 55, normalized size = 1. \begin{align*} \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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^5*(3+5*x)/(1-2*x)^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 = 1.25404, size = 178, normalized size = 3.24 \begin{align*} \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 )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^5*(3+5*x)/(1-2*x)^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 = 0.10367, size = 48, normalized size = 0.87 \begin{align*} \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} \end{align*}

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*log(2*x - 1)/16 - 184877/(256*x
- 128)

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Giac [A]  time = 3.23915, size = 101, normalized size = 1.84 \begin{align*} \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} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^5*(3+5*x)/(1-2*x)^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 + 173215/(2*x - 1)^4 + 81) - 184877/
128/(2*x - 1) - 60025/16*log(1/2*abs(2*x - 1)/(2*x - 1)^2)