3.54.1 \(\int \frac {e^{e^{e^{\frac {x^3}{\log (3-i \pi +x-\log (\frac {23}{3}))}}}+e^{\frac {x^3}{\log (3-i \pi +x-\log (\frac {23}{3}))}}+\frac {x^3}{\log (3-i \pi +x-\log (\frac {23}{3}))}} (x^3+(-9 x^2-3 x^3+3 x^2 (i \pi +\log (\frac {23}{3}))) \log (3-i \pi +x-\log (\frac {23}{3})))}{(-3+i \pi -x+\log (\frac {23}{3})) \log ^2(3-i \pi +x-\log (\frac {23}{3}))} \, dx\)

Optimal. Leaf size=27 \[ e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}} \]

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Rubi [F]  time = 25.69, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\exp \left (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Log[3 - I*Pi + x
- Log[23/3]])*(x^3 + (-9*x^2 - 3*x^3 + 3*x^2*(I*Pi + Log[23/3]))*Log[3 - I*Pi + x - Log[23/3]]))/((-3 + I*Pi
- x + Log[23/3])*Log[3 - I*Pi + x - Log[23/3]]^2),x]

[Out]

3*(Pi + I*(3 - Log[23/3]))^2*Defer[Int][E^(E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x -
Log[23/3]]) + x^3/Log[3 - I*Pi + x - Log[23/3]])/Log[3 - I*Pi + x - Log[23/3]]^2, x] + (3 - I*Pi - Log[23/3])
*Defer[Int][(E^(E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Log[3 -
I*Pi + x - Log[23/3]])*(3 - I*Pi + x - Log[23/3]))/Log[3 - I*Pi + x - Log[23/3]]^2, x] + (6 - (2*I)*Pi - Log[5
29/9])*Defer[Int][(E^(E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Lo
g[3 - I*Pi + x - Log[23/3]])*(3 - I*Pi + x - Log[23/3]))/Log[3 - I*Pi + x - Log[23/3]]^2, x] - Defer[Int][(E^(
E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Log[3 - I*Pi + x - Log[2
3/3]])*(3 - I*Pi + x - Log[23/3])^2)/Log[3 - I*Pi + x - Log[23/3]]^2, x] - (Pi + I*(3 - Log[23/3]))^3*Defer[In
t][E^(E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Log[3 - I*Pi + x -
Log[23/3]])/((3*I + Pi + I*x - I*Log[23/3])*Log[3 - I*Pi + x - Log[23/3]]^2), x] - 3*(Pi + I*(3 - Log[23/3]))
^2*Defer[Int][E^(E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Log[3 -
I*Pi + x - Log[23/3]])/Log[3 - I*Pi + x - Log[23/3]], x] - 3*(6 - (2*I)*Pi - Log[529/9])*Defer[Int][(E^(E^E^(
x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Log[3 - I*Pi + x - Log[23/3]]
)*(3 - I*Pi + x - Log[23/3]))/Log[3 - I*Pi + x - Log[23/3]], x] + 3*Defer[Int][(E^(E^E^(x^3/Log[3 - I*Pi + x -
Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Log[3 - I*Pi + x - Log[23/3]])*(3 - I*Pi + x - Log[
23/3])^2)/Log[3 - I*Pi + x - Log[23/3]], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {\exp \left (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) x^3}{\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}+\frac {3 \exp \left (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) x^2}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) \, dx\\ &=3 \int \frac {\exp \left (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) x^2}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx-\int \frac {\exp \left (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) x^3}{\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.11, size = 27, normalized size = 1.00 \begin {gather*} e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Log[3 - I*
Pi + x - Log[23/3]])*(x^3 + (-9*x^2 - 3*x^3 + 3*x^2*(I*Pi + Log[23/3]))*Log[3 - I*Pi + x - Log[23/3]]))/((-3 +
I*Pi - x + Log[23/3])*Log[3 - I*Pi + x - Log[23/3]]^2),x]

[Out]

E^E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]])

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fricas [A]  time = 0.72, size = 179, normalized size = 6.63 \begin {gather*} \cosh \left (-\cosh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right ) + \sinh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right )\right ) - \sinh \left (-\cosh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right ) + \sinh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^2*(log(23/3)+I*pi)-3*x^3-9*x^2)*log(-log(23/3)-I*pi+3+x)+x^3)*exp(x^3/log(-log(23/3)-I*pi+3+x)
)*exp(exp(x^3/log(-log(23/3)-I*pi+3+x)))*exp(exp(exp(x^3/log(-log(23/3)-I*pi+3+x))))/(log(23/3)+I*pi-3-x)/log(
-log(23/3)-I*pi+3+x)^2,x, algorithm="fricas")

[Out]

cosh(-cosh(-cosh(-x^3/log(-I*pi + x - log(23/3) + 3)) + sinh(-x^3/log(-I*pi + x - log(23/3) + 3))) + sinh(-cos
h(-x^3/log(-I*pi + x - log(23/3) + 3)) + sinh(-x^3/log(-I*pi + x - log(23/3) + 3)))) - sinh(-cosh(-cosh(-x^3/l
og(-I*pi + x - log(23/3) + 3)) + sinh(-x^3/log(-I*pi + x - log(23/3) + 3))) + sinh(-cosh(-x^3/log(-I*pi + x -
log(23/3) + 3)) + sinh(-x^3/log(-I*pi + x - log(23/3) + 3))))

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^2*(log(23/3)+I*pi)-3*x^3-9*x^2)*log(-log(23/3)-I*pi+3+x)+x^3)*exp(x^3/log(-log(23/3)-I*pi+3+x)
)*exp(exp(x^3/log(-log(23/3)-I*pi+3+x)))*exp(exp(exp(x^3/log(-log(23/3)-I*pi+3+x))))/(log(23/3)+I*pi-3-x)/log(
-log(23/3)-I*pi+3+x)^2,x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.47, size = 24, normalized size = 0.89

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x^{3}}{\ln \left (-\ln \left (23\right )+\ln \relax (3)-i \pi +3+x \right )}}}}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*x^2*(ln(23/3)+I*Pi)-3*x^3-9*x^2)*ln(-ln(23/3)-I*Pi+3+x)+x^3)*exp(x^3/ln(-ln(23/3)-I*Pi+3+x))*exp(exp(x
^3/ln(-ln(23/3)-I*Pi+3+x)))*exp(exp(exp(x^3/ln(-ln(23/3)-I*Pi+3+x))))/(ln(23/3)+I*Pi-3-x)/ln(-ln(23/3)-I*Pi+3+
x)^2,x,method=_RETURNVERBOSE)

[Out]

exp(exp(exp(x^3/ln(-ln(23)+ln(3)-I*Pi+3+x))))

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maxima [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^2*(log(23/3)+I*pi)-3*x^3-9*x^2)*log(-log(23/3)-I*pi+3+x)+x^3)*exp(x^3/log(-log(23/3)-I*pi+3+x)
)*exp(exp(x^3/log(-log(23/3)-I*pi+3+x)))*exp(exp(exp(x^3/log(-log(23/3)-I*pi+3+x))))/(log(23/3)+I*pi-3-x)/log(
-log(23/3)-I*pi+3+x)^2,x, algorithm="maxima")

[Out]

Timed out

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^{{\mathrm {e}}^{\frac {x^3}{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}}}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{\frac {x^3}{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}}}}\,{\mathrm {e}}^{\frac {x^3}{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}}\,\left (\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )\,\left (9\,x^2-3\,x^2\,\left (\ln \left (\frac {23}{3}\right )+\Pi \,1{}\mathrm {i}\right )+3\,x^3\right )-x^3\right )}{{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}^2\,\left (\ln \left (\frac {23}{3}\right )-x-3+\Pi \,1{}\mathrm {i}\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(x^3/log(x - Pi*1i - log(23/3) + 3)))*exp(exp(exp(x^3/log(x - Pi*1i - log(23/3) + 3))))*exp(x^3/l
og(x - Pi*1i - log(23/3) + 3))*(log(x - Pi*1i - log(23/3) + 3)*(9*x^2 - 3*x^2*(Pi*1i + log(23/3)) + 3*x^3) - x
^3))/(log(x - Pi*1i - log(23/3) + 3)^2*(Pi*1i - x + log(23/3) - 3)),x)

[Out]

int(-(exp(exp(x^3/log(x - Pi*1i - log(23/3) + 3)))*exp(exp(exp(x^3/log(x - Pi*1i - log(23/3) + 3))))*exp(x^3/l
og(x - Pi*1i - log(23/3) + 3))*(log(x - Pi*1i - log(23/3) + 3)*(9*x^2 - 3*x^2*(Pi*1i + log(23/3)) + 3*x^3) - x
^3))/(log(x - Pi*1i - log(23/3) + 3)^2*(Pi*1i - x + log(23/3) - 3)), x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x**2*(ln(23/3)+I*pi)-3*x**3-9*x**2)*ln(-ln(23/3)-I*pi+3+x)+x**3)*exp(x**3/ln(-ln(23/3)-I*pi+3+x)
)*exp(exp(x**3/ln(-ln(23/3)-I*pi+3+x)))*exp(exp(exp(x**3/ln(-ln(23/3)-I*pi+3+x))))/(ln(23/3)+I*pi-3-x)/ln(-ln(
23/3)-I*pi+3+x)**2,x)

[Out]

Timed out

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