Integrand size = 98, antiderivative size = 25 \begin {dmath*} \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=\frac {4}{5-\left (-4+\frac {4}{3 e^{16} x}\right )^4}+\log (15) \end {dmath*}
Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(25)=50\).
Time = 0.04 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.48 \begin {dmath*} \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=\frac {1024 \left (1-12 e^{16} x+54 e^{32} x^2-108 e^{48} x^3\right )}{251 \left (256-3072 e^{16} x+13824 e^{32} x^2-27648 e^{48} x^3+20331 e^{64} x^4\right )} \end {dmath*}
Integrate[(16*(4 - 12*E^16*x)^4)/(81*E^64*x^4*(-25*x + 75*E^16*x^2 + ((4 - 12*E^16*x)^4*(10*x - 30*E^16*x^2))/(81*E^64*x^4) + ((4 - 12*E^16*x)^8*(-x + 3*E^16*x^2))/(6561*E^128*x^8))),x]
(1024*(1 - 12*E^16*x + 54*E^32*x^2 - 108*E^48*x^3))/(251*(256 - 3072*E^16* x + 13824*E^32*x^2 - 27648*E^48*x^3 + 20331*E^64*x^4))
Leaf count is larger than twice the leaf count of optimal. \(193\) vs. \(2(25)=50\).
Time = 1.39 (sec) , antiderivative size = 193, normalized size of antiderivative = 7.72, number of steps used = 13, number of rules used = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {27, 27, 7239, 27, 2527, 27, 2029, 2527, 27, 2029, 2527, 27, 2021}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (75 e^{16} x^2+\frac {\left (3 e^{16} x^2-x\right ) \left (4-12 e^{16} x\right )^8}{6561 e^{128} x^8}+\frac {\left (10 x-30 e^{16} x^2\right ) \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4}-25 x\right )} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {16 \int -\frac {1679616 \left (1-3 e^{16} x\right )^4}{x^4 \left (\frac {65536 \left (x-3 e^{16} x^2\right ) \left (1-3 e^{16} x\right )^8}{e^{128} x^8}-\frac {207360 \left (x-3 e^{16} x^2\right ) \left (1-3 e^{16} x\right )^4}{e^{64} x^4}-492075 e^{16} x^2+164025 x\right )}dx}{81 e^{64}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\frac {331776 \int \frac {\left (1-3 e^{16} x\right )^4}{x^4 \left (\frac {65536 \left (x-3 e^{16} x^2\right ) \left (1-3 e^{16} x\right )^8}{e^{128} x^8}-\frac {207360 \left (x-3 e^{16} x^2\right ) \left (1-3 e^{16} x\right )^4}{e^{64} x^4}-492075 e^{16} x^2+164025 x\right )}dx}{e^{64}}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {331776 \int \frac {e^{128} x^3 \left (1-3 e^{16} x\right )^3}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx}{e^{64}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -331776 e^{64} \int \frac {x^3 \left (1-3 e^{16} x\right )^3}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle -331776 e^{64} \left (\frac {x^3}{753 e^{16} \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\int \frac {81 \left (-6777 e^{96} x^5+6867 e^{80} x^4-2299 e^{64} x^3+256 e^{48} x^2\right )}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx}{20331 e^{64}}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -331776 e^{64} \left (\frac {x^3}{753 e^{16} \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\int \frac {-6777 e^{96} x^5+6867 e^{80} x^4-2299 e^{64} x^3+256 e^{48} x^2}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx}{251 e^{64}}\right )\) |
| \(\Big \downarrow \) 2029 |
| \(\displaystyle -331776 e^{64} \left (\frac {x^3}{753 e^{16} \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\int \frac {x^2 \left (-6777 e^{96} x^3+6867 e^{80} x^2-2299 e^{64} x+256 e^{48}\right )}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx}{251 e^{64}}\right )\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle -331776 e^{64} \left (\frac {x^3}{753 e^{16} \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\frac {e^{32} x^2}{6 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\int \frac {13554 \left (-6777 e^{144} x^4+6897 e^{128} x^3-2304 e^{112} x^2+256 e^{96} x\right )}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx}{40662 e^{64}}}{251 e^{64}}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -331776 e^{64} \left (\frac {x^3}{753 e^{16} \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\frac {e^{32} x^2}{6 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\int \frac {-6777 e^{144} x^4+6897 e^{128} x^3-2304 e^{112} x^2+256 e^{96} x}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx}{3 e^{64}}}{251 e^{64}}\right )\) |
| \(\Big \downarrow \) 2029 |
| \(\displaystyle -331776 e^{64} \left (\frac {x^3}{753 e^{16} \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\frac {e^{32} x^2}{6 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\int \frac {x \left (-6777 e^{144} x^3+6897 e^{128} x^2-2304 e^{112} x+256 e^{96}\right )}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx}{3 e^{64}}}{251 e^{64}}\right )\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle -331776 e^{64} \left (\frac {x^3}{753 e^{16} \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\frac {e^{32} x^2}{6 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\frac {e^{80} x}{9 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\int \frac {6777 \left (-6777 e^{192} x^3+6912 e^{176} x^2-2304 e^{160} x+256 e^{144}\right )}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx}{60993 e^{64}}}{3 e^{64}}}{251 e^{64}}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -331776 e^{64} \left (\frac {x^3}{753 e^{16} \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\frac {e^{32} x^2}{6 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\frac {e^{80} x}{9 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\int \frac {-6777 e^{192} x^3+6912 e^{176} x^2-2304 e^{160} x+256 e^{144}}{\left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )^2}dx}{9 e^{64}}}{3 e^{64}}}{251 e^{64}}\right )\) |
| \(\Big \downarrow \) 2021 |
| \(\displaystyle -331776 e^{64} \left (\frac {x^3}{753 e^{16} \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\frac {e^{32} x^2}{6 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {\frac {e^{80} x}{9 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}-\frac {e^{64}}{108 \left (20331 e^{64} x^4-27648 e^{48} x^3+13824 e^{32} x^2-3072 e^{16} x+256\right )}}{3 e^{64}}}{251 e^{64}}\right )\) |
Int[(16*(4 - 12*E^16*x)^4)/(81*E^64*x^4*(-25*x + 75*E^16*x^2 + ((4 - 12*E^ 16*x)^4*(10*x - 30*E^16*x^2))/(81*E^64*x^4) + ((4 - 12*E^16*x)^8*(-x + 3*E ^16*x^2))/(6561*E^128*x^8))),x]
-331776*E^64*(x^3/(753*E^16*(256 - 3072*E^16*x + 13824*E^32*x^2 - 27648*E^ 48*x^3 + 20331*E^64*x^4)) - ((E^32*x^2)/(6*(256 - 3072*E^16*x + 13824*E^32 *x^2 - 27648*E^48*x^3 + 20331*E^64*x^4)) - (-1/108*E^64/(256 - 3072*E^16*x + 13824*E^32*x^2 - 27648*E^48*x^3 + 20331*E^64*x^4) + (E^80*x)/(9*(256 - 3072*E^16*x + 13824*E^32*x^2 - 27648*E^48*x^3 + 20331*E^64*x^4)))/(3*E^64) )/(251*E^64))
3.11.74.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Pp_)*(Qq_)^(m_.), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x ]}, Simp[Coeff[Pp, x, p]*x^(p - q + 1)*(Qq^(m + 1)/((p + m*q + 1)*Coeff[Qq, x, q])), x] /; NeQ[p + m*q + 1, 0] && EqQ[(p + m*q + 1)*Coeff[Qq, x, q]*Pp , Coeff[Pp, x, p]*x^(p - q)*((p - q + 1)*Qq + (m + 1)*x*D[Qq, x])]] /; Free Q[m, x] && PolyQ[Pp, x] && PolyQ[Qq, x] && NeQ[m, -1]
Int[(Fx_.)*((d_.)*(x_)^(q_.) + (a_.)*(x_)^(r_.) + (b_.)*(x_)^(s_.) + (c_.)* (x_)^(t_.))^(p_.), x_Symbol] :> Int[x^(p*r)*(a + b*x^(s - r) + c*x^(t - r) + d*x^(q - r))^p*Fx, x] /; FreeQ[{a, b, c, d, r, s, t, q}, x] && IntegerQ[p ] && PosQ[s - r] && PosQ[t - r] && PosQ[q - r] && !(EqQ[p, 1] && EqQ[u, 1] )
Int[(Pm_)*(Qn_)^(p_.), x_Symbol] :> With[{m = Expon[Pm, x], n = Expon[Qn, x ]}, Simp[Coeff[Pm, x, m]*x^(m - n + 1)*(Qn^(p + 1)/((m + n*p + 1)*Coeff[Qn, x, n])), x] + Simp[1/((m + n*p + 1)*Coeff[Qn, x, n]) Int[ExpandToSum[(m + n*p + 1)*Coeff[Qn, x, n]*Pm - Coeff[Pm, x, m]*x^(m - n)*((m - n + 1)*Qn + (p + 1)*x*D[Qn, x]), x]*Qn^p, x], x] /; LtQ[1, n, m + 1] && m + n*p + 1 < 0] /; FreeQ[p, x] && PolyQ[Pm, x] && PolyQ[Qn, x] && LtQ[p, -1]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 2.01 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.84
| method | result | size |
| norman | \(-\frac {324 \,{\mathrm e}^{64} x^{4}}{20331 x^{4} {\mathrm e}^{64}-27648 \,{\mathrm e}^{48} x^{3}+13824 x^{2} {\mathrm e}^{32}-3072 x \,{\mathrm e}^{16}+256}\) | \(46\) |
| parallelrisch | \(-\frac {324 \,{\mathrm e}^{64} x^{4}}{20331 x^{4} {\mathrm e}^{64}-27648 \,{\mathrm e}^{48} x^{3}+13824 x^{2} {\mathrm e}^{32}-3072 x \,{\mathrm e}^{16}+256}\) | \(46\) |
| risch | \(\frac {16 \,{\mathrm e}^{-64} \left (-\frac {6912 \,{\mathrm e}^{112} x^{3}}{63001}+\frac {3456 \,{\mathrm e}^{96} x^{2}}{63001}-\frac {768 \,{\mathrm e}^{80} x}{63001}+\frac {64 \,{\mathrm e}^{64}}{63001}\right )}{81 \left (x^{4} {\mathrm e}^{64}-\frac {1024 \,{\mathrm e}^{48} x^{3}}{753}+\frac {512 x^{2} {\mathrm e}^{32}}{753}-\frac {1024 x \,{\mathrm e}^{16}}{6777}+\frac {256}{20331}\right )}\) | \(58\) |
| gosper | \(-\frac {1024 \left (108 \,{\mathrm e}^{48} x^{3}-54 x^{2} {\mathrm e}^{32}+12 x \,{\mathrm e}^{16}-1\right )}{251 \left (20331 x^{4} {\mathrm e}^{64}-27648 \,{\mathrm e}^{48} x^{3}+13824 x^{2} {\mathrm e}^{32}-3072 x \,{\mathrm e}^{16}+256\right )}\) | \(64\) |
| default | \(13824 \,{\mathrm e}^{64} \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (413349561 \textit {\_Z}^{8} {\mathrm e}^{128}-1124222976 \,{\mathrm e}^{112} \textit {\_Z}^{7}+1326523392 \,{\mathrm e}^{96} \textit {\_Z}^{6}-889325568 \,{\mathrm e}^{80} \textit {\_Z}^{5}+371381760 \textit {\_Z}^{4} {\mathrm e}^{64}-99090432 \,{\mathrm e}^{48} \textit {\_Z}^{3}+16515072 \textit {\_Z}^{2} {\mathrm e}^{32}-1572864 \,{\mathrm e}^{16} \textit {\_Z} +65536\right )}{\sum }\frac {\left (-27 \,{\mathrm e}^{48} \textit {\_R}^{6}+27 \,{\mathrm e}^{32} \textit {\_R}^{5}-9 \,{\mathrm e}^{16} \textit {\_R}^{4}+\textit {\_R}^{3}\right ) \ln \left (x -\textit {\_R} \right )}{-137783187 \textit {\_R}^{7} {\mathrm e}^{128}+327898368 \,{\mathrm e}^{112} \textit {\_R}^{6}-331630848 \,{\mathrm e}^{96} \textit {\_R}^{5}+185276160 \,{\mathrm e}^{80} \textit {\_R}^{4}-61896960 \textit {\_R}^{3} {\mathrm e}^{64}+12386304 \,{\mathrm e}^{48} \textit {\_R}^{2}-1376256 \textit {\_R} \,{\mathrm e}^{32}+65536 \,{\mathrm e}^{16}}\right )\) | \(157\) |
int(16/81*(-12*x*exp(16)+4)^4/x^4/exp(16)^4/(1/6561*(3*x^2*exp(16)-x)*(-12 *x*exp(16)+4)^8/x^8/exp(16)^8+1/81*(-30*x^2*exp(16)+10*x)*(-12*x*exp(16)+4 )^4/x^4/exp(16)^4+75*x^2*exp(16)-25*x),x,method=_RETURNVERBOSE)
-324*exp(16)^4*x^4/(20331*x^4*exp(16)^4-27648*exp(16)^3*x^3+13824*exp(16)^ 2*x^2-3072*x*exp(16)+256)
Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (21) = 42\).
Time = 0.25 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.12 \begin {dmath*} \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=-\frac {1024 \, {\left (108 \, x^{3} e^{48} - 54 \, x^{2} e^{32} + 12 \, x e^{16} - 1\right )}}{251 \, {\left (20331 \, x^{4} e^{64} - 27648 \, x^{3} e^{48} + 13824 \, x^{2} e^{32} - 3072 \, x e^{16} + 256\right )}} \end {dmath*}
integrate(16/81*(-12*x*exp(16)+4)^4/x^4/exp(16)^4/(1/6561*(3*x^2*exp(16)-x )*(-12*x*exp(16)+4)^8/x^8/exp(16)^8+1/81*(-30*x^2*exp(16)+10*x)*(-12*x*exp (16)+4)^4/x^4/exp(16)^4+75*x^2*exp(16)-25*x),x, algorithm=\
-1024/251*(108*x^3*e^48 - 54*x^2*e^32 + 12*x*e^16 - 1)/(20331*x^4*e^64 - 2 7648*x^3*e^48 + 13824*x^2*e^32 - 3072*x*e^16 + 256)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (17) = 34\).
Time = 0.73 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \begin {dmath*} \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=\frac {- 110592 x^{3} e^{48} + 55296 x^{2} e^{32} - 12288 x e^{16} + 1024}{5103081 x^{4} e^{64} - 6939648 x^{3} e^{48} + 3469824 x^{2} e^{32} - 771072 x e^{16} + 64256} \end {dmath*}
integrate(16/81*(-12*x*exp(16)+4)**4/x**4/exp(16)**4/(1/6561*(3*x**2*exp(1 6)-x)*(-12*x*exp(16)+4)**8/x**8/exp(16)**8+1/81*(-30*x**2*exp(16)+10*x)*(- 12*x*exp(16)+4)**4/x**4/exp(16)**4+75*x**2*exp(16)-25*x),x)
(-110592*x**3*exp(48) + 55296*x**2*exp(32) - 12288*x*exp(16) + 1024)/(5103 081*x**4*exp(64) - 6939648*x**3*exp(48) + 3469824*x**2*exp(32) - 771072*x* exp(16) + 64256)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (21) = 42\).
Time = 0.29 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \begin {dmath*} \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=-\frac {1024 \, {\left (108 \, x^{3} e^{112} - 54 \, x^{2} e^{96} + 12 \, x e^{80} - e^{64}\right )} e^{\left (-64\right )}}{251 \, {\left (20331 \, x^{4} e^{64} - 27648 \, x^{3} e^{48} + 13824 \, x^{2} e^{32} - 3072 \, x e^{16} + 256\right )}} \end {dmath*}
integrate(16/81*(-12*x*exp(16)+4)^4/x^4/exp(16)^4/(1/6561*(3*x^2*exp(16)-x )*(-12*x*exp(16)+4)^8/x^8/exp(16)^8+1/81*(-30*x^2*exp(16)+10*x)*(-12*x*exp (16)+4)^4/x^4/exp(16)^4+75*x^2*exp(16)-25*x),x, algorithm=\
-1024/251*(108*x^3*e^112 - 54*x^2*e^96 + 12*x*e^80 - e^64)*e^(-64)/(20331* x^4*e^64 - 27648*x^3*e^48 + 13824*x^2*e^32 - 3072*x*e^16 + 256)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (21) = 42\).
Time = 0.28 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \begin {dmath*} \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=-\frac {1024 \, {\left (108 \, x^{3} e^{112} - 54 \, x^{2} e^{96} + 12 \, x e^{80} - e^{64}\right )} e^{\left (-64\right )}}{251 \, {\left (20331 \, x^{4} e^{64} - 27648 \, x^{3} e^{48} + 13824 \, x^{2} e^{32} - 3072 \, x e^{16} + 256\right )}} \end {dmath*}
integrate(16/81*(-12*x*exp(16)+4)^4/x^4/exp(16)^4/(1/6561*(3*x^2*exp(16)-x )*(-12*x*exp(16)+4)^8/x^8/exp(16)^8+1/81*(-30*x^2*exp(16)+10*x)*(-12*x*exp (16)+4)^4/x^4/exp(16)^4+75*x^2*exp(16)-25*x),x, algorithm=\
-1024/251*(108*x^3*e^112 - 54*x^2*e^96 + 12*x*e^80 - e^64)*e^(-64)/(20331* x^4*e^64 - 27648*x^3*e^48 + 13824*x^2*e^32 - 3072*x*e^16 + 256)
Time = 17.39 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.12 \begin {dmath*} \int \frac {16 \left (4-12 e^{16} x\right )^4}{81 e^{64} x^4 \left (-25 x+75 e^{16} x^2+\frac {\left (4-12 e^{16} x\right )^4 \left (10 x-30 e^{16} x^2\right )}{81 e^{64} x^4}+\frac {\left (4-12 e^{16} x\right )^8 \left (-x+3 e^{16} x^2\right )}{6561 e^{128} x^8}\right )} \, dx=-\frac {\frac {110592\,{\mathrm {e}}^{48}\,x^3}{251}-\frac {55296\,{\mathrm {e}}^{32}\,x^2}{251}+\frac {12288\,{\mathrm {e}}^{16}\,x}{251}-\frac {1024}{251}}{20331\,{\mathrm {e}}^{64}\,x^4-27648\,{\mathrm {e}}^{48}\,x^3+13824\,{\mathrm {e}}^{32}\,x^2-3072\,{\mathrm {e}}^{16}\,x+256} \end {dmath*}
int(-(16*exp(-64)*(12*x*exp(16) - 4)^4)/(81*x^4*(25*x - 75*x^2*exp(16) + ( exp(-128)*(x - 3*x^2*exp(16))*(12*x*exp(16) - 4)^8)/(6561*x^8) - (exp(-64) *(12*x*exp(16) - 4)^4*(10*x - 30*x^2*exp(16)))/(81*x^4))),x)