3.46.17 \(\int \frac {e^{\frac {4}{2+e^{\frac {2}{81} (4-36 \log (x)+81 \log ^2(x))}}} (72+18 e^{\frac {4}{81} (4-36 \log (x)+81 \log ^2(x))}+e^{\frac {2}{81} (4-36 \log (x)+81 \log ^2(x))} (136-288 \log (x)))}{36 \log (2)+36 e^{\frac {2}{81} (4-36 \log (x)+81 \log ^2(x))} \log (2)+9 e^{\frac {4}{81} (4-36 \log (x)+81 \log ^2(x))} \log (2)} \, dx\) [4517]

Optimal. Leaf size=27 \[ \frac {2 e^{\frac {4}{2+e^{2 \left (-\frac {2}{9}+\log (x)\right )^2}}} x}{\log (2)} \]

[Out]

2*x*exp(4/(2+exp((ln(x)-2/9)^2)^2))/ln(2)

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Rubi [F]
time = 43.35, 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 {e^{\frac {4}{2+e^{\frac {2}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )}}} \left (72+18 e^{\frac {4}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )}+e^{\frac {2}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )} (136-288 \log (x))\right )}{36 \log (2)+36 e^{\frac {2}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )} \log (2)+9 e^{\frac {4}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )} \log (2)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(4/(2 + E^((2*(4 - 36*Log[x] + 81*Log[x]^2))/81)))*(72 + 18*E^((4*(4 - 36*Log[x] + 81*Log[x]^2))/81) +
E^((2*(4 - 36*Log[x] + 81*Log[x]^2))/81)*(136 - 288*Log[x])))/(36*Log[2] + 36*E^((2*(4 - 36*Log[x] + 81*Log[x]
^2))/81)*Log[2] + 9*E^((4*(4 - 36*Log[x] + 81*Log[x]^2))/81)*Log[2]),x]

[Out]

(18*Defer[Subst][Defer[Int][E^(4/(2 + E^(8/81 + 2*Log[x^9]^2)/x^8))*x^8, x], x, x^(1/9)])/Log[2] - (128*Defer[
Subst][Defer[Int][(E^(4/(2 + E^(8/81 + 2*Log[x^9]^2)/(x^9)^(8/9)))*x^24)/(E^(8/81 + 2*Log[x^9]^2) + 2*x^8)^2,
x], x, x^(1/9)])/Log[2] + (64*Defer[Subst][Defer[Int][(E^(4/(2 + E^(8/81 + 2*Log[x^9]^2)/(x^9)^(8/9)))*x^16)/(
E^(8/81 + 2*Log[x^9]^2) + 2*x^8), x], x, x^(1/9)])/Log[2] + (576*Defer[Subst][Defer[Int][(E^(4/(2 + E^(8/81 +
2*Log[x^9]^2)/(x^9)^(8/9)))*x^24*Log[x^9])/(E^(8/81 + 2*Log[x^9]^2) + 2*x^8)^2, x], x, x^(1/9)])/Log[2] - (288
*Defer[Subst][Defer[Int][(E^(4/(2 + E^(8/81 + 2*Log[x^9]^2)/(x^9)^(8/9)))*x^16*Log[x^9])/(E^(8/81 + 2*Log[x^9]
^2) + 2*x^8), x], x, x^(1/9)])/Log[2]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {4}{2+e^{\frac {2}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )}}} x^{16/9} \left (72+18 e^{\frac {4}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )}+e^{\frac {2}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )} (136-288 \log (x))\right )}{9 \left (e^{\frac {8}{81}+2 \log ^2(x)}+2 x^{8/9}\right )^2 \log (2)} \, dx\\ &=\frac {\int \frac {e^{\frac {4}{2+e^{\frac {2}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )}}} x^{16/9} \left (72+18 e^{\frac {4}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )}+e^{\frac {2}{81} \left (4-36 \log (x)+81 \log ^2(x)\right )} (136-288 \log (x))\right )}{\left (e^{\frac {8}{81}+2 \log ^2(x)}+2 x^{8/9}\right )^2} \, dx}{9 \log (2)}\\ &=\frac {\text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{24} \left (72+\frac {18 e^{\frac {16}{81}+4 \log ^2\left (x^9\right )}}{\left (x^9\right )^{16/9}}-\frac {8 e^{\frac {8}{81}+2 \log ^2\left (x^9\right )} \left (-17+36 \log \left (x^9\right )\right )}{\left (x^9\right )^{8/9}}\right )}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}\\ &=\frac {\text {Subst}\left (\int \left (18 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^6 \left (x^9\right )^{2/9}-\frac {8 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{15} \left (9 x^8-17 \left (x^9\right )^{8/9}+36 \left (x^9\right )^{8/9} \log \left (x^9\right )\right )}{\left (x^9\right )^{7/9} \left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )}+\frac {8 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{23} \left (9 x^8+9 x \left (x^9\right )^{7/9}-34 \left (x^9\right )^{8/9}+72 \left (x^9\right )^{8/9} \log \left (x^9\right )\right )}{\left (x^9\right )^{7/9} \left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2}\right ) \, dx,x,\sqrt [9]{x}\right )}{\log (2)}\\ &=-\frac {8 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{15} \left (9 x^8-17 \left (x^9\right )^{8/9}+36 \left (x^9\right )^{8/9} \log \left (x^9\right )\right )}{\left (x^9\right )^{7/9} \left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {8 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{23} \left (9 x^8+9 x \left (x^9\right )^{7/9}-34 \left (x^9\right )^{8/9}+72 \left (x^9\right )^{8/9} \log \left (x^9\right )\right )}{\left (x^9\right )^{7/9} \left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {18 \text {Subst}\left (\int e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^6 \left (x^9\right )^{2/9} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}\\ &=-\frac {8 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^8 \left (9 x^8-17 \left (x^9\right )^{8/9}+36 \left (x^9\right )^{8/9} \log \left (x^9\right )\right )}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {8 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16} \left (9 x^8+9 x \left (x^9\right )^{7/9}-34 \left (x^9\right )^{8/9}+72 \left (x^9\right )^{8/9} \log \left (x^9\right )\right )}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {18 \text {Subst}\left (\int e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^8 \, dx,x,\sqrt [9]{x}\right )}{\log (2)}\\ &=\frac {2 \text {Subst}\left (\int e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2(x)}}{x^{8/9}}}} \, dx,x,x\right )}{\log (2)}+\frac {8 \text {Subst}\left (\int \left (\frac {9 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{24}}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2}+\frac {9 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{17} \left (x^9\right )^{7/9}}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2}-\frac {34 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16} \left (x^9\right )^{8/9}}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2}+\frac {72 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16} \left (x^9\right )^{8/9} \log \left (x^9\right )}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2}\right ) \, dx,x,\sqrt [9]{x}\right )}{\log (2)}-\frac {8 \text {Subst}\left (\int \left (\frac {9 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16}}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8}-\frac {17 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^8 \left (x^9\right )^{8/9}}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8}+\frac {36 e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^8 \left (x^9\right )^{8/9} \log \left (x^9\right )}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8}\right ) \, dx,x,\sqrt [9]{x}\right )}{\log (2)}\\ &=\frac {18 \text {Subst}\left (\int e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{x^8}}} x^8 \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {72 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{24}}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {72 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{17} \left (x^9\right )^{7/9}}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}-\frac {72 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16}}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {136 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^8 \left (x^9\right )^{8/9}}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}-\frac {272 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16} \left (x^9\right )^{8/9}}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}-\frac {288 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^8 \left (x^9\right )^{8/9} \log \left (x^9\right )}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {576 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16} \left (x^9\right )^{8/9} \log \left (x^9\right )}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}\\ &=\frac {18 \text {Subst}\left (\int e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{x^8}}} x^8 \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+2 \frac {72 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{24}}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}-\frac {72 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16}}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {136 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16}}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}-\frac {272 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{24}}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}-\frac {288 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{16} \log \left (x^9\right )}{e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}+\frac {576 \text {Subst}\left (\int \frac {e^{\frac {4}{2+\frac {e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}}{\left (x^9\right )^{8/9}}}} x^{24} \log \left (x^9\right )}{\left (e^{\frac {8}{81}+2 \log ^2\left (x^9\right )}+2 x^8\right )^2} \, dx,x,\sqrt [9]{x}\right )}{\log (2)}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.22, size = 38, normalized size = 1.41 \begin {gather*} \frac {2 e^{\frac {4 x^{8/9}}{e^{\frac {8}{81}+2 \log ^2(x)}+2 x^{8/9}}} x}{\log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(4/(2 + E^((2*(4 - 36*Log[x] + 81*Log[x]^2))/81)))*(72 + 18*E^((4*(4 - 36*Log[x] + 81*Log[x]^2))/
81) + E^((2*(4 - 36*Log[x] + 81*Log[x]^2))/81)*(136 - 288*Log[x])))/(36*Log[2] + 36*E^((2*(4 - 36*Log[x] + 81*
Log[x]^2))/81)*Log[2] + 9*E^((4*(4 - 36*Log[x] + 81*Log[x]^2))/81)*Log[2]),x]

[Out]

(2*E^((4*x^(8/9))/(E^(8/81 + 2*Log[x]^2) + 2*x^(8/9)))*x)/Log[2]

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Maple [A]
time = 1.73, size = 31, normalized size = 1.15

method	result	size
risch	\(\frac {2 x \,{\mathrm e}^{\frac {4 x^{\frac {8}{9}}}{2 x^{\frac {8}{9}}+{\mathrm e}^{2 \ln \left (x \right )^{2}+\frac {8}{81}}}}}{\ln \left (2\right )}\)	\(31\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((18*exp(ln(x)^2-4/9*ln(x)+4/81)^4+(-288*ln(x)+136)*exp(ln(x)^2-4/9*ln(x)+4/81)^2+72)*exp(4/(exp(ln(x)^2-4/
9*ln(x)+4/81)^2+2))/(9*ln(2)*exp(ln(x)^2-4/9*ln(x)+4/81)^4+36*ln(2)*exp(ln(x)^2-4/9*ln(x)+4/81)^2+36*ln(2)),x,
method=_RETURNVERBOSE)

[Out]

2*x/ln(2)*exp(4*x^(8/9)/(2*x^(8/9)+exp(2*ln(x)^2+8/81)))

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Maxima [A]
time = 0.69, size = 30, normalized size = 1.11 \begin {gather*} \frac {2 \, x e^{\left (\frac {4 \, x^{\frac {8}{9}}}{2 \, x^{\frac {8}{9}} + e^{\left (2 \, \log \left (x\right )^{2} + \frac {8}{81}\right )}}\right )}}{\log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((18*exp(log(x)^2-4/9*log(x)+4/81)^4+(-288*log(x)+136)*exp(log(x)^2-4/9*log(x)+4/81)^2+72)*exp(4/(exp
(log(x)^2-4/9*log(x)+4/81)^2+2))/(9*log(2)*exp(log(x)^2-4/9*log(x)+4/81)^4+36*log(2)*exp(log(x)^2-4/9*log(x)+4
/81)^2+36*log(2)),x, algorithm="maxima")

[Out]

2*x*e^(4*x^(8/9)/(2*x^(8/9) + e^(2*log(x)^2 + 8/81)))/log(2)

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Fricas [A]
time = 0.35, size = 27, normalized size = 1.00 \begin {gather*} \frac {2 \, x e^{\left (\frac {4}{e^{\left (2 \, \log \left (x\right )^{2} - \frac {8}{9} \, \log \left (x\right ) + \frac {8}{81}\right )} + 2}\right )}}{\log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((18*exp(log(x)^2-4/9*log(x)+4/81)^4+(-288*log(x)+136)*exp(log(x)^2-4/9*log(x)+4/81)^2+72)*exp(4/(exp
(log(x)^2-4/9*log(x)+4/81)^2+2))/(9*log(2)*exp(log(x)^2-4/9*log(x)+4/81)^4+36*log(2)*exp(log(x)^2-4/9*log(x)+4
/81)^2+36*log(2)),x, algorithm="fricas")

[Out]

2*x*e^(4/(e^(2*log(x)^2 - 8/9*log(x) + 8/81) + 2))/log(2)

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Sympy [F(-1)] Timed out
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((18*exp(ln(x)**2-4/9*ln(x)+4/81)**4+(-288*ln(x)+136)*exp(ln(x)**2-4/9*ln(x)+4/81)**2+72)*exp(4/(exp(
ln(x)**2-4/9*ln(x)+4/81)**2+2))/(9*ln(2)*exp(ln(x)**2-4/9*ln(x)+4/81)**4+36*ln(2)*exp(ln(x)**2-4/9*ln(x)+4/81)
**2+36*ln(2)),x)

[Out]

Timed out

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Giac [F(-1)] Timed out
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((18*exp(log(x)^2-4/9*log(x)+4/81)^4+(-288*log(x)+136)*exp(log(x)^2-4/9*log(x)+4/81)^2+72)*exp(4/(exp
(log(x)^2-4/9*log(x)+4/81)^2+2))/(9*log(2)*exp(log(x)^2-4/9*log(x)+4/81)^4+36*log(2)*exp(log(x)^2-4/9*log(x)+4
/81)^2+36*log(2)),x, algorithm="giac")

[Out]

Timed out

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Mupad [B]
time = 3.61, size = 27, normalized size = 1.00 \begin {gather*} \frac {2\,x\,{\mathrm {e}}^{\frac {4}{\frac {{\mathrm {e}}^{2\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{8/81}}{x^{8/9}}+2}}}{\ln \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(4/(exp(2*log(x)^2 - (8*log(x))/9 + 8/81) + 2))*(18*exp(4*log(x)^2 - (16*log(x))/9 + 16/81) - exp(2*lo
g(x)^2 - (8*log(x))/9 + 8/81)*(288*log(x) - 136) + 72))/(36*log(2) + 36*exp(2*log(x)^2 - (8*log(x))/9 + 8/81)*
log(2) + 9*exp(4*log(x)^2 - (16*log(x))/9 + 16/81)*log(2)),x)

[Out]

(2*x*exp(4/((exp(2*log(x)^2)*exp(8/81))/x^(8/9) + 2)))/log(2)

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