3.1633 \(\int \frac{(2+3 x)^5 (3+5 x)}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=59 \[ -\frac{1215 x^4}{32}-\frac{4401 x^3}{16}-\frac{16821 x^2}{16}-\frac{109089 x}{32}-\frac{60025}{16 (1-2 x)}+\frac{184877}{256 (1-2 x)^2}-\frac{519645}{128} \log (1-2 x) \]

[Out]

184877/(256*(1 - 2*x)^2) - 60025/(16*(1 - 2*x)) - (109089*x)/32 - (16821*x^2)/16 - (4401*x^3)/16 - (1215*x^4)/
32 - (519645*Log[1 - 2*x])/128

________________________________________________________________________________________

Rubi [A]  time = 0.0304676, antiderivative size = 59, 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} \[ -\frac{1215 x^4}{32}-\frac{4401 x^3}{16}-\frac{16821 x^2}{16}-\frac{109089 x}{32}-\frac{60025}{16 (1-2 x)}+\frac{184877}{256 (1-2 x)^2}-\frac{519645}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

184877/(256*(1 - 2*x)^2) - 60025/(16*(1 - 2*x)) - (109089*x)/32 - (16821*x^2)/16 - (4401*x^3)/16 - (1215*x^4)/
32 - (519645*Log[1 - 2*x])/128

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)^3} \, dx &=\int \left (-\frac{109089}{32}-\frac{16821 x}{8}-\frac{13203 x^2}{16}-\frac{1215 x^3}{8}-\frac{184877}{64 (-1+2 x)^3}-\frac{60025}{8 (-1+2 x)^2}-\frac{519645}{64 (-1+2 x)}\right ) \, dx\\ &=\frac{184877}{256 (1-2 x)^2}-\frac{60025}{16 (1-2 x)}-\frac{109089 x}{32}-\frac{16821 x^2}{16}-\frac{4401 x^3}{16}-\frac{1215 x^4}{32}-\frac{519645}{128} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0155942, size = 56, normalized size = 0.95 \[ -\frac{77760 x^6+485568 x^5+1609200 x^4+4969440 x^3-10547820 x^2+2008220 x+2078580 (1-2 x)^2 \log (1-2 x)+524947}{512 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-(524947 + 2008220*x - 10547820*x^2 + 4969440*x^3 + 1609200*x^4 + 485568*x^5 + 77760*x^6 + 2078580*(1 - 2*x)^2
*Log[1 - 2*x])/(512*(1 - 2*x)^2)

________________________________________________________________________________________

Maple [A]  time = 0.007, size = 46, normalized size = 0.8 \begin{align*} -{\frac{1215\,{x}^{4}}{32}}-{\frac{4401\,{x}^{3}}{16}}-{\frac{16821\,{x}^{2}}{16}}-{\frac{109089\,x}{32}}-{\frac{519645\,\ln \left ( 2\,x-1 \right ) }{128}}+{\frac{184877}{256\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{60025}{32\,x-16}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1215/32*x^4-4401/16*x^3-16821/16*x^2-109089/32*x-519645/128*ln(2*x-1)+184877/256/(2*x-1)^2+60025/16/(2*x-1)

________________________________________________________________________________________

Maxima [A]  time = 1.58624, size = 62, normalized size = 1.05 \begin{align*} -\frac{1215}{32} \, x^{4} - \frac{4401}{16} \, x^{3} - \frac{16821}{16} \, x^{2} - \frac{109089}{32} \, x + \frac{2401 \,{\left (800 \, x - 323\right )}}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{519645}{128} \, \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)^3,x, algorithm="maxima")

[Out]

-1215/32*x^4 - 4401/16*x^3 - 16821/16*x^2 - 109089/32*x + 2401/256*(800*x - 323)/(4*x^2 - 4*x + 1) - 519645/12
8*log(2*x - 1)

________________________________________________________________________________________

Fricas [A]  time = 1.36479, size = 208, normalized size = 3.53 \begin{align*} -\frac{38880 \, x^{6} + 242784 \, x^{5} + 804600 \, x^{4} + 2484720 \, x^{3} - 3221712 \, x^{2} + 1039290 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1048088 \, x + 775523}{256 \,{\left (4 \, x^{2} - 4 \, 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)^3,x, algorithm="fricas")

[Out]

-1/256*(38880*x^6 + 242784*x^5 + 804600*x^4 + 2484720*x^3 - 3221712*x^2 + 1039290*(4*x^2 - 4*x + 1)*log(2*x -
1) - 1048088*x + 775523)/(4*x^2 - 4*x + 1)

________________________________________________________________________________________

Sympy [A]  time = 0.125577, size = 49, normalized size = 0.83 \begin{align*} - \frac{1215 x^{4}}{32} - \frac{4401 x^{3}}{16} - \frac{16821 x^{2}}{16} - \frac{109089 x}{32} + \frac{1920800 x - 775523}{1024 x^{2} - 1024 x + 256} - \frac{519645 \log{\left (2 x - 1 \right )}}{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)**3,x)

[Out]

-1215*x**4/32 - 4401*x**3/16 - 16821*x**2/16 - 109089*x/32 + (1920800*x - 775523)/(1024*x**2 - 1024*x + 256) -
519645*log(2*x - 1)/128

________________________________________________________________________________________

Giac [A]  time = 3.56673, size = 57, normalized size = 0.97 \begin{align*} -\frac{1215}{32} \, x^{4} - \frac{4401}{16} \, x^{3} - \frac{16821}{16} \, x^{2} - \frac{109089}{32} \, x + \frac{2401 \,{\left (800 \, x - 323\right )}}{256 \,{\left (2 \, x - 1\right )}^{2}} - \frac{519645}{128} \, \log \left ({\left | 2 \, x - 1 \right |}\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)^3,x, algorithm="giac")

[Out]

-1215/32*x^4 - 4401/16*x^3 - 16821/16*x^2 - 109089/32*x + 2401/256*(800*x - 323)/(2*x - 1)^2 - 519645/128*log(
abs(2*x - 1))