Integrand size = 115, antiderivative size = 24 \[ \int \frac {e^{\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}} \left (-9-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx=e^{\frac {9 x}{\left (-3+e^e\right ) (4 x+x \log (2))^2}} x \]
Time = 0.07 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {e^{\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}} \left (-9-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx=e^{\frac {9}{\left (-3+e^e\right ) x (4+\log (2))^2}} x \]
Integrate[(E^(9/(-48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8*x*Log[ 2] + x*Log[2]^2)))*(-9 - 48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8 *x*Log[2] + x*Log[2]^2)))/(-48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8*x*Log[2] + x*Log[2]^2)),x]
Time = 0.65 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {6, 6, 6, 6, 2026, 25, 6, 25, 27, 2726}
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.
| \(\displaystyle \int \frac {\left (-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)-9\right ) \exp \left (\frac {9}{-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)}\right )}{-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )+x (-48-24 \log (2))-9\right ) \exp \left (\frac {9}{-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)}\right )}{-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (x \left (-48-3 \log ^2(2)-24 \log (2)\right )+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-9\right ) \exp \left (\frac {9}{-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)}\right )}{-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (x \left (-48-3 \log ^2(2)-24 \log (2)\right )+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-9\right ) \exp \left (\frac {9}{-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)}\right )}{-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )+x (-48-24 \log (2))}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (x \left (-48-3 \log ^2(2)-24 \log (2)\right )+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-9\right ) \exp \left (\frac {9}{-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)}\right )}{x \left (-48-3 \log ^2(2)-24 \log (2)\right )+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )}dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int -\frac {\left (x \left (-48-3 \log ^2(2)-24 \log (2)\right )+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-9\right ) \exp \left (\frac {9}{-48 x-3 x \log ^2(2)+e^e \left (16 x+x \log ^2(2)+8 x \log (2)\right )-24 x \log (2)}\right )}{\left (3-e^e\right ) x (4+\log (2))^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\int -\frac {e^{-\frac {9}{\left (3-e^e\right ) x (4+\log (2))^2}} \left (-e^e (4+\log (2))^2 x+3 (4+\log (2))^2 x+9\right )}{\left (3-e^e\right ) x (4+\log (2))^2}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle -\int -\frac {e^{-\frac {9}{\left (3-e^e\right ) x (4+\log (2))^2}} \left (\left (3-e^e\right ) (4+\log (2))^2 x+9\right )}{\left (3-e^e\right ) x (4+\log (2))^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle \int \frac {e^{-\frac {9}{\left (3-e^e\right ) x (4+\log (2))^2}} \left (\left (3-e^e\right ) x (4+\log (2))^2+9\right )}{\left (3-e^e\right ) x (4+\log (2))^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \frac {e^{-\frac {9}{\left (3-e^e\right ) x (4+\log (2))^2}} \left (\left (3-e^e\right ) (4+\log (2))^2 x+9\right )}{x}dx}{\left (3-e^e\right ) (4+\log (2))^2}\) |
| \(\Big \downarrow \) 2726 |
| \(\displaystyle x e^{-\frac {9}{\left (3-e^e\right ) x (4+\log (2))^2}}\) |
Int[(E^(9/(-48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8*x*Log[2] + x *Log[2]^2)))*(-9 - 48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8*x*Log [2] + x*Log[2]^2)))/(-48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8*x* Log[2] + x*Log[2]^2)),x]
3.3.84.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = v*(y/(Log[F]*D[u, x]))}, Simp[F^u*z, x] /; EqQ[D[z, x], w*y]] /; FreeQ[F, x]
Time = 0.74 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92
| method | result | size |
| risch | \(x \,{\mathrm e}^{\frac {9}{x \left (4+\ln \left (2\right )\right )^{2} \left ({\mathrm e}^{{\mathrm e}}-3\right )}}\) | \(22\) |
| gosper | \(x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \left (2\right )^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \left (2\right )-3 \ln \left (2\right )^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \left (2\right )-48\right )}}\) | \(43\) |
| norman | \(x \,{\mathrm e}^{\frac {9}{\left (x \ln \left (2\right )^{2}+8 x \ln \left (2\right )+16 x \right ) {\mathrm e}^{{\mathrm e}}-3 x \ln \left (2\right )^{2}-24 x \ln \left (2\right )-48 x}}\) | \(43\) |
| parallelrisch | \(\frac {{\mathrm e}^{{\mathrm e}} \ln \left (2\right )^{2} x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \left (2\right )^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \left (2\right )-3 \ln \left (2\right )^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \left (2\right )-48\right )}}+8 \,{\mathrm e}^{{\mathrm e}} \ln \left (2\right ) x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \left (2\right )^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \left (2\right )-3 \ln \left (2\right )^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \left (2\right )-48\right )}}-3 \ln \left (2\right )^{2} x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \left (2\right )^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \left (2\right )-3 \ln \left (2\right )^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \left (2\right )-48\right )}}+16 \,{\mathrm e}^{{\mathrm e}} x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \left (2\right )^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \left (2\right )-3 \ln \left (2\right )^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \left (2\right )-48\right )}}-24 \ln \left (2\right ) x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \left (2\right )^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \left (2\right )-3 \ln \left (2\right )^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \left (2\right )-48\right )}}-48 x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \left (2\right )^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \left (2\right )-3 \ln \left (2\right )^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \left (2\right )-48\right )}}}{{\mathrm e}^{{\mathrm e}} \ln \left (2\right )^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \left (2\right )-3 \ln \left (2\right )^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \left (2\right )-48}\) | \(315\) |
| derivativedivides | \(\text {Expression too large to display}\) | \(1029\) |
| default | \(\text {Expression too large to display}\) | \(1029\) |
int(((x*ln(2)^2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)^2-24*x*ln(2)-48*x-9) *exp(9/((x*ln(2)^2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)^2-24*x*ln(2)-48*x ))/((x*ln(2)^2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)^2-24*x*ln(2)-48*x),x, method=_RETURNVERBOSE)
Time = 0.26 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.79 \[ \int \frac {e^{\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}} \left (-9-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx=x e^{\left (-\frac {9}{3 \, x \log \left (2\right )^{2} - {\left (x \log \left (2\right )^{2} + 8 \, x \log \left (2\right ) + 16 \, x\right )} e^{e} + 24 \, x \log \left (2\right ) + 48 \, x}\right )} \]
integrate(((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24*x*log( 2)-48*x-9)*exp(9/((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24 *x*log(2)-48*x))/((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24 *x*log(2)-48*x),x, algorithm=\
Time = 0.16 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.83 \[ \int \frac {e^{\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}} \left (-9-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx=x e^{\frac {9}{- 48 x - 24 x \log {\left (2 \right )} - 3 x \log {\left (2 \right )}^{2} + \left (x \log {\left (2 \right )}^{2} + 8 x \log {\left (2 \right )} + 16 x\right ) e^{e}}} \]
integrate(((x*ln(2)**2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)**2-24*x*ln(2) -48*x-9)*exp(9/((x*ln(2)**2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)**2-24*x* ln(2)-48*x))/((x*ln(2)**2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)**2-24*x*ln (2)-48*x),x)
Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.46 (sec) , antiderivative size = 266, normalized size of antiderivative = 11.08 \[ \int \frac {e^{\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}} \left (-9-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx=\frac {9 \, {\rm Ei}\left (\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \left (2\right ) + 4\right )}^{2}}\right )}{{\left (e^{e} - 3\right )} {\left (\log \left (2\right ) + 4\right )}^{2}} - \frac {9 \, e^{e} \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \left (2\right ) + 4\right )}^{2}}\right ) \log \left (2\right )^{2}}{{\left (e^{e} - 3\right )}^{2} {\left (\log \left (2\right ) + 4\right )}^{4}} - \frac {72 \, e^{e} \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \left (2\right ) + 4\right )}^{2}}\right ) \log \left (2\right )}{{\left (e^{e} - 3\right )}^{2} {\left (\log \left (2\right ) + 4\right )}^{4}} + \frac {27 \, \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \left (2\right ) + 4\right )}^{2}}\right ) \log \left (2\right )^{2}}{{\left (e^{e} - 3\right )}^{2} {\left (\log \left (2\right ) + 4\right )}^{4}} - \frac {144 \, e^{e} \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \left (2\right ) + 4\right )}^{2}}\right )}{{\left (e^{e} - 3\right )}^{2} {\left (\log \left (2\right ) + 4\right )}^{4}} + \frac {216 \, \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \left (2\right ) + 4\right )}^{2}}\right ) \log \left (2\right )}{{\left (e^{e} - 3\right )}^{2} {\left (\log \left (2\right ) + 4\right )}^{4}} + \frac {432 \, \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \left (2\right ) + 4\right )}^{2}}\right )}{{\left (e^{e} - 3\right )}^{2} {\left (\log \left (2\right ) + 4\right )}^{4}} \]
integrate(((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24*x*log( 2)-48*x-9)*exp(9/((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24 *x*log(2)-48*x))/((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24 *x*log(2)-48*x),x, algorithm=\
9*Ei(9/(x*(e^e - 3)*(log(2) + 4)^2))/((e^e - 3)*(log(2) + 4)^2) - 9*e^e*ga mma(-1, -9/(x*(e^e - 3)*(log(2) + 4)^2))*log(2)^2/((e^e - 3)^2*(log(2) + 4 )^4) - 72*e^e*gamma(-1, -9/(x*(e^e - 3)*(log(2) + 4)^2))*log(2)/((e^e - 3) ^2*(log(2) + 4)^4) + 27*gamma(-1, -9/(x*(e^e - 3)*(log(2) + 4)^2))*log(2)^ 2/((e^e - 3)^2*(log(2) + 4)^4) - 144*e^e*gamma(-1, -9/(x*(e^e - 3)*(log(2) + 4)^2))/((e^e - 3)^2*(log(2) + 4)^4) + 216*gamma(-1, -9/(x*(e^e - 3)*(lo g(2) + 4)^2))*log(2)/((e^e - 3)^2*(log(2) + 4)^4) + 432*gamma(-1, -9/(x*(e ^e - 3)*(log(2) + 4)^2))/((e^e - 3)^2*(log(2) + 4)^4)
Leaf count of result is larger than twice the leaf count of optimal. 806 vs. \(2 (23) = 46\).
Time = 0.48 (sec) , antiderivative size = 806, normalized size of antiderivative = 33.58 \[ \int \frac {e^{\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}} \left (-9-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx=\text {Too large to display} \]
integrate(((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24*x*log( 2)-48*x-9)*exp(9/((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24 *x*log(2)-48*x))/((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24 *x*log(2)-48*x),x, algorithm=\
(e^e*log(2)^2 + 8*e^e*log(2) - 3*log(2)^2 + 16*e^e - 24*log(2) - 48)*e^(9/ (x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x))/(e^(2*e)*log(2)^4/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) - 6*e^e*log(2)^4/(x*e^e*log(2)^2 + 8*x*e^ e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 16*e^(2*e)*log( 2)^3/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log (2) - 48*x) - 96*e^e*log(2)^3/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2 )^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 9*log(2)^4/(x*e^e*log(2)^2 + 8*x*e^ e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 96*e^(2*e)*log( 2)^2/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log (2) - 48*x) - 576*e^e*log(2)^2/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log( 2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 144*log(2)^3/(x*e^e*log(2)^2 + 8*x *e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 256*e^(2*e)* log(2)/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*l og(2) - 48*x) - 1536*e^e*log(2)/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log (2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 864*log(2)^2/(x*e^e*log(2)^2 + 8* x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 256*e^(2*e) /(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) - 1536*e^e/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x* e^e - 24*x*log(2) - 48*x) + 2304*log(2)/(x*e^e*log(2)^2 + 8*x*e^e*log(2...
Time = 12.04 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.96 \[ \int \frac {e^{\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}} \left (-9-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx=x\,{\mathrm {e}}^{-\frac {9}{48\,x+24\,x\,\ln \left (2\right )-16\,x\,{\mathrm {e}}^{\mathrm {e}}+3\,x\,{\ln \left (2\right )}^2-8\,x\,{\mathrm {e}}^{\mathrm {e}}\,\ln \left (2\right )-x\,{\mathrm {e}}^{\mathrm {e}}\,{\ln \left (2\right )}^2}} \]
int((exp(-9/(48*x + 24*x*log(2) - exp(exp(1))*(16*x + 8*x*log(2) + x*log(2 )^2) + 3*x*log(2)^2))*(48*x + 24*x*log(2) - exp(exp(1))*(16*x + 8*x*log(2) + x*log(2)^2) + 3*x*log(2)^2 + 9))/(48*x + 24*x*log(2) - exp(exp(1))*(16* x + 8*x*log(2) + x*log(2)^2) + 3*x*log(2)^2),x)