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

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Rubi [A]  time = 0.03, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}

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Mathematica [A]  time = 0.02, 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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fricas [A]  time = 0.86, size = 52, normalized size = 0.95 \[ \frac {15552 \, x^{6} + 88128 \, x^{5} + 240480 \, x^{4} + 459360 \, x^{3} + 904080 \, x^{2} + 480200 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 602934 \, x - 184877}{128 \, {\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((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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giac [A]  time = 1.21, size = 75, normalized size = 1.36 \[ \frac {3}{128} \, {\left (2 \, x - 1\right )}^{5} {\left (\frac {1404}{2 \, x - 1} + \frac {10815}{{\left (2 \, x - 1\right )}^{2}} + \frac {49980}{{\left (2 \, x - 1\right )}^{3}} + \frac {173215}{{\left (2 \, x - 1\right )}^{4}} + 81\right )} - \frac {184877}{128 \, {\left (2 \, x - 1\right )}} - \frac {60025}{16} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \]

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)

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maple [A]  time = 0.01, size = 42, normalized size = 0.76 \[ \frac {243 x^{5}}{4}+\frac {2997 x^{4}}{8}+\frac {18027 x^{3}}{16}+\frac {75447 x^{2}}{32}+\frac {301467 x}{64}+\frac {60025 \ln \left (2 x -1\right )}{16}-\frac {184877}{128 \left (2 x -1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x+2)^5*(5*x+3)/(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/(2*x-1)+60025/16*ln(2*x-1)

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maxima [A]  time = 0.48, size = 41, normalized size = 0.75 \[ \frac {243}{4} \, x^{5} + \frac {2997}{8} \, x^{4} + \frac {18027}{16} \, x^{3} + \frac {75447}{32} \, x^{2} + \frac {301467}{64} \, x - \frac {184877}{128 \, {\left (2 \, x - 1\right )}} + \frac {60025}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((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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mupad [B]  time = 0.03, size = 39, normalized size = 0.71 \[ \frac {301467\,x}{64}+\frac {60025\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {184877}{256\,\left (x-\frac {1}{2}\right )}+\frac {75447\,x^2}{32}+\frac {18027\,x^3}{16}+\frac {2997\,x^4}{8}+\frac {243\,x^5}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.12, 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*log(2*x - 1)/16 - 184877/(256*x
- 128)

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