3.1660 \(\int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=73 \[ -\frac{10125 x^6}{16}-\frac{80595 x^5}{16}-\frac{629505 x^4}{32}-\frac{1661133 x^3}{32}-\frac{28504029 x^2}{256}-\frac{64029233 x}{256}-\frac{39220335}{256 (1-2 x)}+\frac{22370117}{1024 (1-2 x)^2}-\frac{60160485}{256} \log (1-2 x) \]

[Out]

22370117/(1024*(1 - 2*x)^2) - 39220335/(256*(1 - 2*x)) - (64029233*x)/256 - (28504029*x^2)/256 - (1661133*x^3)
/32 - (629505*x^4)/32 - (80595*x^5)/16 - (10125*x^6)/16 - (60160485*Log[1 - 2*x])/256

________________________________________________________________________________________

Rubi [A]  time = 0.0382232, antiderivative size = 73, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{10125 x^6}{16}-\frac{80595 x^5}{16}-\frac{629505 x^4}{32}-\frac{1661133 x^3}{32}-\frac{28504029 x^2}{256}-\frac{64029233 x}{256}-\frac{39220335}{256 (1-2 x)}+\frac{22370117}{1024 (1-2 x)^2}-\frac{60160485}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

22370117/(1024*(1 - 2*x)^2) - 39220335/(256*(1 - 2*x)) - (64029233*x)/256 - (28504029*x^2)/256 - (1661133*x^3)
/32 - (629505*x^4)/32 - (80595*x^5)/16 - (10125*x^6)/16 - (60160485*Log[1 - 2*x])/256

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac{64029233}{256}-\frac{28504029 x}{128}-\frac{4983399 x^2}{32}-\frac{629505 x^3}{8}-\frac{402975 x^4}{16}-\frac{30375 x^5}{8}-\frac{22370117}{256 (-1+2 x)^3}-\frac{39220335}{128 (-1+2 x)^2}-\frac{60160485}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{22370117}{1024 (1-2 x)^2}-\frac{39220335}{256 (1-2 x)}-\frac{64029233 x}{256}-\frac{28504029 x^2}{256}-\frac{1661133 x^3}{32}-\frac{629505 x^4}{32}-\frac{80595 x^5}{16}-\frac{10125 x^6}{16}-\frac{60160485}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0211286, size = 66, normalized size = 0.9 \[ -\frac{2592000 x^8+18040320 x^7+60592320 x^6+137206464 x^5+263583600 x^4+621559520 x^3-1569001020 x^2+600903660 x+240641940 (1-2 x)^2 \log (1-2 x)-30126129}{1024 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-(-30126129 + 600903660*x - 1569001020*x^2 + 621559520*x^3 + 263583600*x^4 + 137206464*x^5 + 60592320*x^6 + 18
040320*x^7 + 2592000*x^8 + 240641940*(1 - 2*x)^2*Log[1 - 2*x])/(1024*(1 - 2*x)^2)

________________________________________________________________________________________

Maple [A]  time = 0.006, size = 56, normalized size = 0.8 \begin{align*} -{\frac{10125\,{x}^{6}}{16}}-{\frac{80595\,{x}^{5}}{16}}-{\frac{629505\,{x}^{4}}{32}}-{\frac{1661133\,{x}^{3}}{32}}-{\frac{28504029\,{x}^{2}}{256}}-{\frac{64029233\,x}{256}}-{\frac{60160485\,\ln \left ( 2\,x-1 \right ) }{256}}+{\frac{22370117}{1024\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{39220335}{512\,x-256}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10125/16*x^6-80595/16*x^5-629505/32*x^4-1661133/32*x^3-28504029/256*x^2-64029233/256*x-60160485/256*ln(2*x-1)
[phone]/1024/(2*x-1)^2+39220335/256/(2*x-1)

________________________________________________________________________________________

Maxima [A]  time = 1.81977, size = 76, normalized size = 1.04 \begin{align*} -\frac{10125}{16} \, x^{6} - \frac{80595}{16} \, x^{5} - \frac{629505}{32} \, x^{4} - \frac{1661133}{32} \, x^{3} - \frac{28504029}{256} \, x^{2} - \frac{64029233}{256} \, x + \frac{290521 \,{\left (1080 \, x - 463\right )}}{1024 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{60160485}{256} \, \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)^3/(1-2*x)^3,x, algorithm="maxima")

[Out]

-10125/16*x^6 - 80595/16*x^5 - 629505/32*x^4 - 1661133/32*x^3 - 28504029/256*x^2 - 64029233/256*x + 290521/102
4*(1080*x - 463)/(4*x^2 - 4*x + 1) - 60160485/256*log(2*x - 1)

________________________________________________________________________________________

Fricas [A]  time = 1.46917, size = 274, normalized size = 3.75 \begin{align*} -\frac{2592000 \, x^{8} + 18040320 \, x^{7} + 60592320 \, x^{6} + 137206464 \, x^{5} + 263583600 \, x^{4} + 621559520 \, x^{3} - 910451612 \, x^{2} + 240641940 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 57645748 \, x + 134511223}{1024 \,{\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)^3/(1-2*x)^3,x, algorithm="fricas")

[Out]

-1/1024*(2592000*x^8 + 18040320*x^7 + 60592320*x^6 + 137206464*x^5 + 263583600*x^4 + 621559520*x^3 - 910451612
*x^2 + 240641940*(4*x^2 - 4*x + 1)*log(2*x - 1) - 57645748*x + 134511223)/(4*x^2 - 4*x + 1)

________________________________________________________________________________________

Sympy [A]  time = 0.135292, size = 63, normalized size = 0.86 \begin{align*} - \frac{10125 x^{6}}{16} - \frac{80595 x^{5}}{16} - \frac{629505 x^{4}}{32} - \frac{1661133 x^{3}}{32} - \frac{28504029 x^{2}}{256} - \frac{64029233 x}{256} + \frac{313762680 x - 134511223}{4096 x^{2} - 4096 x + 1024} - \frac{60160485 \log{\left (2 x - 1 \right )}}{256} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10125*x**6/16 - 80595*x**5/16 - 629505*x**4/32 - 1661133*x**3/32 - 28504029*x**2/256 - 64029233*x/256 + (3137
62680*x - 134511223)/(4096*x**2 - 4096*x + 1024) - 60160485*log(2*x - 1)/256

________________________________________________________________________________________

Giac [A]  time = 2.23665, size = 70, normalized size = 0.96 \begin{align*} -\frac{10125}{16} \, x^{6} - \frac{80595}{16} \, x^{5} - \frac{629505}{32} \, x^{4} - \frac{1661133}{32} \, x^{3} - \frac{28504029}{256} \, x^{2} - \frac{64029233}{256} \, x + \frac{290521 \,{\left (1080 \, x - 463\right )}}{1024 \,{\left (2 \, x - 1\right )}^{2}} - \frac{60160485}{256} \, \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)^3/(1-2*x)^3,x, algorithm="giac")

[Out]

-10125/16*x^6 - 80595/16*x^5 - 629505/32*x^4 - 1661133/32*x^3 - 28504029/256*x^2 - 64029233/256*x + 290521/102
4*(1080*x - 463)/(2*x - 1)^2 - 60160485/256*log(abs(2*x - 1))