\(\int \frac {1}{3} (-3-64 e^{\frac {4}{3} (x+(i \pi +\log (2))^2)}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} (x+(i \pi +\log (2))^2)} \log ^2(4)+64 e^{\frac {1}{3} (x+(i \pi +\log (2))^2)} \log ^3(4)) \, dx\) [1005]

Optimal result

Integrand size = 92, antiderivative size = 32 \[ \int \frac {1}{3} \left (-3-64 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4)\right ) \, dx=4-x-16 \left (-e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )}+\log (4)\right )^4 \]

[Out]

4-16*(2*ln(2)-exp(1/3*(ln(2)+I*Pi)^2+1/3*x))^4-x

Rubi [B] (verified)

Both result and optimal contain complex but leaf count is larger than twice the leaf count of optimal. \(90\) vs. \(2(32)=64\).

Time = 0.03 (sec) , antiderivative size = 90, normalized size of antiderivative = 2.81, number of steps used = 6, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {12, 2225} \[ \int \frac {1}{3} \left (-3-64 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4)\right ) \, dx=-x+64 \log ^3(4) e^{\frac {1}{3} \left (x+(\log (2)+i \pi )^2\right )}-96 \log ^2(4) e^{\frac {2}{3} \left (x+(\log (2)+i \pi )^2\right )}-16 e^{\frac {4}{3} \left (x+(\log (2)+i \pi )^2\right )}+64 \log (4) e^{x+(\log (2)+i \pi )^2} \]

[In]

Int[(-3 - 64*E^((4*(x + (I*Pi + Log[2])^2))/3) + 192*E^(x + (I*Pi + Log[2])^2)*Log[4] - 192*E^((2*(x + (I*Pi +
Log[2])^2))/3)*Log[4]^2 + 64*E^((x + (I*Pi + Log[2])^2)/3)*Log[4]^3)/3,x]

[Out]

-16*E^((4*(x + (I*Pi + Log[2])^2))/3) - x + 64*E^(x + (I*Pi + Log[2])^2)*Log[4] - 96*E^((2*(x + (I*Pi + Log[2]
)^2))/3)*Log[4]^2 + 64*E^((x + (I*Pi + Log[2])^2)/3)*Log[4]^3

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \int \left (-3-64 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4)\right ) \, dx \\ & = -x-\frac {64}{3} \int e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )} \, dx+(64 \log (4)) \int e^{x+(i \pi +\log (2))^2} \, dx-\left (64 \log ^2(4)\right ) \int e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \, dx+\frac {1}{3} \left (64 \log ^3(4)\right ) \int e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \, dx \\ & = -16 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}-x+64 e^{x+(i \pi +\log (2))^2} \log (4)-96 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4) \\ \end{align*}

Mathematica [B] (verified)

Both result and optimal contain complex but leaf count is larger than twice the leaf count of optimal. \(150\) vs. \(2(32)=64\).

Time = 0.41 (sec) , antiderivative size = 150, normalized size of antiderivative = 4.69 \[ \int \frac {1}{3} \left (-3-64 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4)\right ) \, dx=\frac {1}{3} \left (-3 2^{4+\frac {8 i \pi }{3}} e^{-\frac {4 \pi ^2}{3}+\frac {4 x}{3}+\frac {4 \log ^2(2)}{3}}-3 x+3\ 2^{6+2 i \pi } e^{-\pi ^2+x+\log ^2(2)} \log (4)-9\ 2^{5+\frac {4 i \pi }{3}} e^{-\frac {2 \pi ^2}{3}+\frac {2 x}{3}+\frac {2 \log ^2(2)}{3}} \log ^2(4)+3\ 2^{6+\frac {2 i \pi }{3}} e^{-\frac {\pi ^2}{3}+\frac {x}{3}+\frac {\log ^2(2)}{3}} \log ^3(4)\right ) \]

[In]

Integrate[(-3 - 64*E^((4*(x + (I*Pi + Log[2])^2))/3) + 192*E^(x + (I*Pi + Log[2])^2)*Log[4] - 192*E^((2*(x + (
I*Pi + Log[2])^2))/3)*Log[4]^2 + 64*E^((x + (I*Pi + Log[2])^2)/3)*Log[4]^3)/3,x]

[Out]

(-3*2^(4 + ((8*I)/3)*Pi)*E^((-4*Pi^2)/3 + (4*x)/3 + (4*Log[2]^2)/3) - 3*x + 3*2^(6 + (2*I)*Pi)*E^(-Pi^2 + x +
Log[2]^2)*Log[4] - 9*2^(5 + ((4*I)/3)*Pi)*E^((-2*Pi^2)/3 + (2*x)/3 + (2*Log[2]^2)/3)*Log[4]^2 + 3*2^(6 + ((2*I
)/3)*Pi)*E^(-1/3*Pi^2 + x/3 + Log[2]^2/3)*Log[4]^3)/3

Maple [B] (verified)

Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (32 ) = 64\).

Time = 0.16 (sec) , antiderivative size = 93, normalized size of antiderivative = 2.91

method	result	size
default	\(-x -16 \,{\mathrm e}^{\frac {4 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {4 x}{3}}+128 \ln \left (2\right ) {\mathrm e}^{\left (\ln \left (2\right )+i \pi \right )^{2}+x}-384 \ln \left (2\right )^{2} {\mathrm e}^{\frac {2 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {2 x}{3}}+512 \ln \left (2\right )^{3} {\mathrm e}^{\frac {\left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {x}{3}}\)	\(93\)
norman	\(-x -16 \,{\mathrm e}^{\frac {4 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {4 x}{3}}+128 \ln \left (2\right ) {\mathrm e}^{\left (\ln \left (2\right )+i \pi \right )^{2}+x}-384 \ln \left (2\right )^{2} {\mathrm e}^{\frac {2 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {2 x}{3}}+512 \ln \left (2\right )^{3} {\mathrm e}^{\frac {\left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {x}{3}}\)	\(93\)
parallelrisch	\(-x -16 \,{\mathrm e}^{\frac {4 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {4 x}{3}}+128 \ln \left (2\right ) {\mathrm e}^{\left (\ln \left (2\right )+i \pi \right )^{2}+x}-384 \ln \left (2\right )^{2} {\mathrm e}^{\frac {2 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {2 x}{3}}+512 \ln \left (2\right )^{3} {\mathrm e}^{\frac {\left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {x}{3}}\)	\(93\)
parts	\(-x -16 \,{\mathrm e}^{\frac {4 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {4 x}{3}}+128 \ln \left (2\right ) {\mathrm e}^{\left (\ln \left (2\right )+i \pi \right )^{2}+x}-384 \ln \left (2\right )^{2} {\mathrm e}^{\frac {2 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {2 x}{3}}+512 \ln \left (2\right )^{3} {\mathrm e}^{\frac {\left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {x}{3}}\)	\(93\)
derivativedivides	\(-16 \,{\mathrm e}^{\frac {4 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {4 x}{3}}+128 \ln \left (2\right ) {\mathrm e}^{\left (\ln \left (2\right )+i \pi \right )^{2}+x}-384 \ln \left (2\right )^{2} {\mathrm e}^{\frac {2 \left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {2 x}{3}}+512 \ln \left (2\right )^{3} {\mathrm e}^{\frac {\left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {x}{3}}-3 \ln \left ({\mathrm e}^{\frac {\left (\ln \left (2\right )+i \pi \right )^{2}}{3}+\frac {x}{3}}\right )\)	\(109\)
risch	\(-x -16 \,2^{\frac {8 i \pi }{3}} {\mathrm e}^{-\frac {4 \pi ^{2}}{3}+\frac {4 \ln \left (2\right )^{2}}{3}+\frac {4 x}{3}}+128 \ln \left (2\right ) 2^{2 i \pi } {\mathrm e}^{-\pi ^{2}+\ln \left (2\right )^{2}+x}-384 \ln \left (2\right )^{2} 2^{\frac {4 i \pi }{3}} {\mathrm e}^{-\frac {2 \pi ^{2}}{3}+\frac {2 \ln \left (2\right )^{2}}{3}+\frac {2 x}{3}}+512 \ln \left (2\right )^{3} 2^{\frac {2 i \pi }{3}} {\mathrm e}^{-\frac {\pi ^{2}}{3}+\frac {\ln \left (2\right )^{2}}{3}+\frac {x}{3}}\)	\(113\)

[In]

int(-64/3*exp(1/3*(ln(2)+I*Pi)^2+1/3*x)^4+128*ln(2)*exp(1/3*(ln(2)+I*Pi)^2+1/3*x)^3-256*ln(2)^2*exp(1/3*(ln(2)
+I*Pi)^2+1/3*x)^2+512/3*ln(2)^3*exp(1/3*(ln(2)+I*Pi)^2+1/3*x)-1,x,method=_RETURNVERBOSE)

[Out]

-x-16*exp(1/3*(ln(2)+I*Pi)^2+1/3*x)^4+128*ln(2)*exp(1/3*(ln(2)+I*Pi)^2+1/3*x)^3-384*ln(2)^2*exp(1/3*(ln(2)+I*P
i)^2+1/3*x)^2+512*ln(2)^3*exp(1/3*(ln(2)+I*Pi)^2+1/3*x)

Fricas [B] (verification not implemented)

Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (35) = 70\).

Time = 0.29 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.19 \[ \int \frac {1}{3} \left (-3-64 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4)\right ) \, dx=512 \, e^{\left (-\frac {1}{3} \, \pi ^{2} + \frac {2}{3} i \, \pi \log \left (2\right ) + \frac {1}{3} \, \log \left (2\right )^{2} + \frac {1}{3} \, x\right )} \log \left (2\right )^{3} - 384 \, e^{\left (-\frac {2}{3} \, \pi ^{2} + \frac {4}{3} i \, \pi \log \left (2\right ) + \frac {2}{3} \, \log \left (2\right )^{2} + \frac {2}{3} \, x\right )} \log \left (2\right )^{2} + 128 \, e^{\left (-\pi ^{2} + 2 i \, \pi \log \left (2\right ) + \log \left (2\right )^{2} + x\right )} \log \left (2\right ) - x - 16 \, e^{\left (-\frac {4}{3} \, \pi ^{2} + \frac {8}{3} i \, \pi \log \left (2\right ) + \frac {4}{3} \, \log \left (2\right )^{2} + \frac {4}{3} \, x\right )} \]

[In]

integrate(-64/3*exp(1/3*(log(2)+I*pi)^2+1/3*x)^4+128*log(2)*exp(1/3*(log(2)+I*pi)^2+1/3*x)^3-256*log(2)^2*exp(
1/3*(log(2)+I*pi)^2+1/3*x)^2+512/3*log(2)^3*exp(1/3*(log(2)+I*pi)^2+1/3*x)-1,x, algorithm="fricas")

[Out]

512*e^(-1/3*pi^2 + 2/3*I*pi*log(2) + 1/3*log(2)^2 + 1/3*x)*log(2)^3 - 384*e^(-2/3*pi^2 + 4/3*I*pi*log(2) + 2/3
*log(2)^2 + 2/3*x)*log(2)^2 + 128*e^(-pi^2 + 2*I*pi*log(2) + log(2)^2 + x)*log(2) - x - 16*e^(-4/3*pi^2 + 8/3*
I*pi*log(2) + 4/3*log(2)^2 + 4/3*x)

Sympy [B] (verification not implemented)

Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 163 vs. \(2 (26) = 52\).

Time = 0.16 (sec) , antiderivative size = 163, normalized size of antiderivative = 5.09 \[ \int \frac {1}{3} \left (-3-64 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4)\right ) \, dx=- x + \frac {- 16 e^{2 \pi ^{2}} e^{\frac {4 x}{3}} e^{\frac {8 i \pi \log {\left (2 \right )}}{3}} e^{\frac {4 \log {\left (2 \right )}^{2}}{3}} - 384 e^{\frac {8 \pi ^{2}}{3}} e^{\frac {2 x}{3}} e^{\frac {4 i \pi \log {\left (2 \right )}}{3}} e^{\frac {2 \log {\left (2 \right )}^{2}}{3}} \log {\left (2 \right )}^{2} + 512 e^{3 \pi ^{2}} e^{\frac {x}{3}} e^{\frac {2 i \pi \log {\left (2 \right )}}{3}} e^{\frac {\log {\left (2 \right )}^{2}}{3}} \log {\left (2 \right )}^{3} + 128 e^{\frac {7 \pi ^{2}}{3}} e^{x} e^{2 i \pi \log {\left (2 \right )}} e^{\log {\left (2 \right )}^{2}} \log {\left (2 \right )}}{e^{\frac {10 \pi ^{2}}{3}}} \]

[In]

integrate(-64/3*exp(1/3*(ln(2)+I*pi)**2+1/3*x)**4+128*ln(2)*exp(1/3*(ln(2)+I*pi)**2+1/3*x)**3-256*ln(2)**2*exp
(1/3*(ln(2)+I*pi)**2+1/3*x)**2+512/3*ln(2)**3*exp(1/3*(ln(2)+I*pi)**2+1/3*x)-1,x)

[Out]

-x + (-16*exp(2*pi**2)*exp(4*x/3)*exp(8*I*pi*log(2)/3)*exp(4*log(2)**2/3) - 384*exp(8*pi**2/3)*exp(2*x/3)*exp(
4*I*pi*log(2)/3)*exp(2*log(2)**2/3)*log(2)**2 + 512*exp(3*pi**2)*exp(x/3)*exp(2*I*pi*log(2)/3)*exp(log(2)**2/3
)*log(2)**3 + 128*exp(7*pi**2/3)*exp(x)*exp(2*I*pi*log(2))*exp(log(2)**2)*log(2))*exp(-10*pi**2/3)

Maxima [B] (verification not implemented)

Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (35) = 70\).

Time = 0.18 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.19 \[ \int \frac {1}{3} \left (-3-64 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4)\right ) \, dx=512 \, e^{\left (-\frac {1}{3} \, \pi ^{2} + \frac {2}{3} i \, \pi \log \left (2\right ) + \frac {1}{3} \, \log \left (2\right )^{2} + \frac {1}{3} \, x\right )} \log \left (2\right )^{3} - 384 \, e^{\left (-\frac {2}{3} \, \pi ^{2} + \frac {4}{3} i \, \pi \log \left (2\right ) + \frac {2}{3} \, \log \left (2\right )^{2} + \frac {2}{3} \, x\right )} \log \left (2\right )^{2} + 128 \, e^{\left (-\pi ^{2} + 2 i \, \pi \log \left (2\right ) + \log \left (2\right )^{2} + x\right )} \log \left (2\right ) - x - 16 \, e^{\left (-\frac {4}{3} \, \pi ^{2} + \frac {8}{3} i \, \pi \log \left (2\right ) + \frac {4}{3} \, \log \left (2\right )^{2} + \frac {4}{3} \, x\right )} \]

[In]

integrate(-64/3*exp(1/3*(log(2)+I*pi)^2+1/3*x)^4+128*log(2)*exp(1/3*(log(2)+I*pi)^2+1/3*x)^3-256*log(2)^2*exp(
1/3*(log(2)+I*pi)^2+1/3*x)^2+512/3*log(2)^3*exp(1/3*(log(2)+I*pi)^2+1/3*x)-1,x, algorithm="maxima")

[Out]

512*e^(-1/3*pi^2 + 2/3*I*pi*log(2) + 1/3*log(2)^2 + 1/3*x)*log(2)^3 - 384*e^(-2/3*pi^2 + 4/3*I*pi*log(2) + 2/3
*log(2)^2 + 2/3*x)*log(2)^2 + 128*e^(-pi^2 + 2*I*pi*log(2) + log(2)^2 + x)*log(2) - x - 16*e^(-4/3*pi^2 + 8/3*
I*pi*log(2) + 4/3*log(2)^2 + 4/3*x)

Giac [B] (verification not implemented)

Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (35) = 70\).

Time = 0.26 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.19 \[ \int \frac {1}{3} \left (-3-64 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4)\right ) \, dx=512 \, e^{\left (-\frac {1}{3} \, \pi ^{2} + \frac {2}{3} i \, \pi \log \left (2\right ) + \frac {1}{3} \, \log \left (2\right )^{2} + \frac {1}{3} \, x\right )} \log \left (2\right )^{3} - 384 \, e^{\left (-\frac {2}{3} \, \pi ^{2} + \frac {4}{3} i \, \pi \log \left (2\right ) + \frac {2}{3} \, \log \left (2\right )^{2} + \frac {2}{3} \, x\right )} \log \left (2\right )^{2} + 128 \, e^{\left (-\pi ^{2} + 2 i \, \pi \log \left (2\right ) + \log \left (2\right )^{2} + x\right )} \log \left (2\right ) - x - 16 \, e^{\left (-\frac {4}{3} \, \pi ^{2} + \frac {8}{3} i \, \pi \log \left (2\right ) + \frac {4}{3} \, \log \left (2\right )^{2} + \frac {4}{3} \, x\right )} \]

[In]

integrate(-64/3*exp(1/3*(log(2)+I*pi)^2+1/3*x)^4+128*log(2)*exp(1/3*(log(2)+I*pi)^2+1/3*x)^3-256*log(2)^2*exp(
1/3*(log(2)+I*pi)^2+1/3*x)^2+512/3*log(2)^3*exp(1/3*(log(2)+I*pi)^2+1/3*x)-1,x, algorithm="giac")

[Out]

512*e^(-1/3*pi^2 + 2/3*I*pi*log(2) + 1/3*log(2)^2 + 1/3*x)*log(2)^3 - 384*e^(-2/3*pi^2 + 4/3*I*pi*log(2) + 2/3
*log(2)^2 + 2/3*x)*log(2)^2 + 128*e^(-pi^2 + 2*I*pi*log(2) + log(2)^2 + x)*log(2) - x - 16*e^(-4/3*pi^2 + 8/3*
I*pi*log(2) + 4/3*log(2)^2 + 4/3*x)

Mupad [B] (verification not implemented)

Time = 9.32 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.31 \[ \int \frac {1}{3} \left (-3-64 e^{\frac {4}{3} \left (x+(i \pi +\log (2))^2\right )}+192 e^{x+(i \pi +\log (2))^2} \log (4)-192 e^{\frac {2}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^2(4)+64 e^{\frac {1}{3} \left (x+(i \pi +\log (2))^2\right )} \log ^3(4)\right ) \, dx=-x-16\,2^{\frac {\Pi \,8{}\mathrm {i}}{3}}\,{\mathrm {e}}^{-\frac {4\,\Pi ^2}{3}+\frac {4\,x}{3}+\frac {4\,{\ln \left (2\right )}^2}{3}}+512\,2^{\frac {\Pi \,2{}\mathrm {i}}{3}}\,{\mathrm {e}}^{-\frac {\Pi ^2}{3}+\frac {x}{3}+\frac {{\ln \left (2\right )}^2}{3}}\,{\ln \left (2\right )}^3-384\,2^{\frac {\Pi \,4{}\mathrm {i}}{3}}\,{\mathrm {e}}^{-\frac {2\,\Pi ^2}{3}+\frac {2\,x}{3}+\frac {2\,{\ln \left (2\right )}^2}{3}}\,{\ln \left (2\right )}^2+128\,2^{\Pi \,2{}\mathrm {i}}\,{\mathrm {e}}^{-\Pi ^2+x+{\ln \left (2\right )}^2}\,\ln \left (2\right ) \]

[In]

int((512*exp(x/3 + (Pi*1i + log(2))^2/3)*log(2)^3)/3 - (64*exp((4*x)/3 + (4*(Pi*1i + log(2))^2)/3))/3 - 256*ex
p((2*x)/3 + (2*(Pi*1i + log(2))^2)/3)*log(2)^2 + 128*exp(x + (Pi*1i + log(2))^2)*log(2) - 1,x)

[Out]

512*2^((Pi*2i)/3)*exp(x/3 - Pi^2/3 + log(2)^2/3)*log(2)^3 - 16*2^((Pi*8i)/3)*exp((4*x)/3 - (4*Pi^2)/3 + (4*log
(2)^2)/3) - x - 384*2^((Pi*4i)/3)*exp((2*x)/3 - (2*Pi^2)/3 + (2*log(2)^2)/3)*log(2)^2 + 128*2^(Pi*2i)*exp(x -
Pi^2 + log(2)^2)*log(2)