3.32.0 ∫ −131072−65536e4−2x2+(−32768−16384e4) log(2)+(−3072−1536e4) log2(2)+(−128−64e4) log3(2)+(−2−e4) log4(2)+4x2 log(x) (65536x+16384x log(2)+1536x log2(2)+64x log3(2)+x log4(2)) log2(x) dx [3106]

Integrand size = 101, antiderivative size = 21 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {2+e^4+\frac {2 x^2}{(16+\log (2))^4}}{\log (x)} \]

Rubi [A] (veriﬁed)

Time = 0.35 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.24, number of steps used = 17, number of rules used = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.099, Rules used = {6, 12, 6820, 6874, 2395, 2343, 2346, 2209, 2339, 30} \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {2 x^2}{(16+\log (2))^4 \log (x)}+\frac {2+e^4}{\log (x)} \]

Rubi steps \begin{align*} \text {integral}& = \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)+x (65536+16384 \log (2))\right ) \log ^2(x)} \, dx \\ & = \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (x \log ^4(2)+x (65536+16384 \log (2))+x \left (1536 \log ^2(2)+64 \log ^3(2)\right )\right ) \log ^2(x)} \, dx \\ & = \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (x \left (1536 \log ^2(2)+64 \log ^3(2)\right )+x \left (65536+16384 \log (2)+\log ^4(2)\right )\right ) \log ^2(x)} \, dx \\ & = \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{x \left (65536+16384 \log (2)+1536 \log ^2(2)+64 \log ^3(2)+\log ^4(2)\right ) \log ^2(x)} \, dx \\ & = \frac {\int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{x \log ^2(x)} \, dx}{(16+\log (2))^4} \\ & = \frac {\int \frac {-e^4 (16+\log (2))^4-2 \left (x^2+(16+\log (2))^4\right )+4 x^2 \log (x)}{x \log ^2(x)} \, dx}{(16+\log (2))^4} \\ & = \frac {\int \left (\frac {-131072-65536 e^4-2 x^2-32768 \log (2)-16384 e^4 \log (2)-3072 \log ^2(2)-1536 e^4 \log ^2(2)-128 \log ^3(2)-64 e^4 \log ^3(2)-2 \log ^4(2)-e^4 \log ^4(2)}{x \log ^2(x)}+\frac {4 x}{\log (x)}\right ) \, dx}{(16+\log (2))^4} \\ & = \frac {\int \frac {-131072-65536 e^4-2 x^2-32768 \log (2)-16384 e^4 \log (2)-3072 \log ^2(2)-1536 e^4 \log ^2(2)-128 \log ^3(2)-64 e^4 \log ^3(2)-2 \log ^4(2)-e^4 \log ^4(2)}{x \log ^2(x)} \, dx}{(16+\log (2))^4}+\frac {4 \int \frac {x}{\log (x)} \, dx}{(16+\log (2))^4} \\ & = \frac {\int \left (-\frac {2 x}{\log ^2(x)}+\frac {-131072-65536 e^4-32768 \log (2)-16384 e^4 \log (2)-3072 \log ^2(2)-1536 e^4 \log ^2(2)-128 \log ^3(2)-64 e^4 \log ^3(2)-2 \log ^4(2)-e^4 \log ^4(2)}{x \log ^2(x)}\right ) \, dx}{(16+\log (2))^4}+\frac {4 \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )}{(16+\log (2))^4} \\ & = \frac {4 \text {Ei}(2 \log (x))}{(16+\log (2))^4}+\left (-2-e^4\right ) \int \frac {1}{x \log ^2(x)} \, dx-\frac {2 \int \frac {x}{\log ^2(x)} \, dx}{(16+\log (2))^4} \\ & = \frac {4 \text {Ei}(2 \log (x))}{(16+\log (2))^4}+\frac {2 x^2}{(16+\log (2))^4 \log (x)}+\left (-2-e^4\right ) \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right )-\frac {4 \int \frac {x}{\log (x)} \, dx}{(16+\log (2))^4} \\ & = \frac {4 \text {Ei}(2 \log (x))}{(16+\log (2))^4}+\frac {2+e^4}{\log (x)}+\frac {2 x^2}{(16+\log (2))^4 \log (x)}-\frac {4 \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )}{(16+\log (2))^4} \\ & = \frac {2+e^4}{\log (x)}+\frac {2 x^2}{(16+\log (2))^4 \log (x)} \\ \end{align*}

Mathematica [A] (veriﬁed)

Time = 0.31 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.62 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {e^4 (16+\log (2))^4+2 \left (x^2+(16+\log (2))^4\right )}{(16+\log (2))^4 \log (x)} \]

Maple [B] (veriﬁed)

Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs. \(2(20)=40\).

Time = 0.19 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.14


method	result	size

norman	\(\frac {\frac {2 x^{2}}{16+\ln \left (2\right )}+8192+{\mathrm e}^{4} \ln \left (2\right )^{3}+48 \,{\mathrm e}^{4} \ln \left (2\right )^{2}+2 \ln \left (2\right )^{3}+768 \,{\mathrm e}^{4} \ln \left (2\right )+96 \ln \left (2\right )^{2}+4096 \,{\mathrm e}^{4}+1536 \ln \left (2\right )}{\left (16+\ln \left (2\right )\right )^{3} \ln \left (x \right )}\)	\(66\)
risch	\(\frac {{\mathrm e}^{4} \ln \left (2\right )^{4}+64 \,{\mathrm e}^{4} \ln \left (2\right )^{3}+2 \ln \left (2\right )^{4}+1536 \,{\mathrm e}^{4} \ln \left (2\right )^{2}+128 \ln \left (2\right )^{3}+16384 \,{\mathrm e}^{4} \ln \left (2\right )+3072 \ln \left (2\right )^{2}+2 x^{2}+65536 \,{\mathrm e}^{4}+32768 \ln \left (2\right )+131072}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}\)	\(92\)
parallelrisch	\(\frac {{\mathrm e}^{4} \ln \left (2\right )^{4}+64 \,{\mathrm e}^{4} \ln \left (2\right )^{3}+2 \ln \left (2\right )^{4}+1536 \,{\mathrm e}^{4} \ln \left (2\right )^{2}+128 \ln \left (2\right )^{3}+16384 \,{\mathrm e}^{4} \ln \left (2\right )+3072 \ln \left (2\right )^{2}+2 x^{2}+65536 \,{\mathrm e}^{4}+32768 \ln \left (2\right )+131072}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}\)	\(92\)
parts	\(-\frac {4 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )}{\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536}-\frac {-\frac {{\mathrm e}^{4} \ln \left (2\right )^{4}}{\ln \left (x \right )}-\frac {64 \,{\mathrm e}^{4} \ln \left (2\right )^{3}}{\ln \left (x \right )}-\frac {2 \ln \left (2\right )^{4}}{\ln \left (x \right )}-\frac {1536 \,{\mathrm e}^{4} \ln \left (2\right )^{2}}{\ln \left (x \right )}-\frac {128 \ln \left (2\right )^{3}}{\ln \left (x \right )}-\frac {16384 \,{\mathrm e}^{4} \ln \left (2\right )}{\ln \left (x \right )}-\frac {3072 \ln \left (2\right )^{2}}{\ln \left (x \right )}-\frac {2 x^{2}}{\ln \left (x \right )}-4 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )-\frac {65536 \,{\mathrm e}^{4}}{\ln \left (x \right )}-\frac {32768 \ln \left (2\right )}{\ln \left (x \right )}-\frac {131072}{\ln \left (x \right )}}{\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536}\)	\(176\)
default	\(\frac {{\mathrm e}^{4} \ln \left (2\right )^{4}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {64 \,{\mathrm e}^{4} \ln \left (2\right )^{3}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {2 \ln \left (2\right )^{4}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}-\frac {4 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )}{\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536}+\frac {1536 \,{\mathrm e}^{4} \ln \left (2\right )^{2}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {128 \ln \left (2\right )^{3}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {16384 \,{\mathrm e}^{4} \ln \left (2\right )}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {3072 \ln \left (2\right )^{2}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}-\frac {2 \left (-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )}{\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536}+\frac {65536 \,{\mathrm e}^{4}}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {32768 \ln \left (2\right )}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}+\frac {131072}{\left (\ln \left (2\right )^{4}+64 \ln \left (2\right )^{3}+1536 \ln \left (2\right )^{2}+16384 \ln \left (2\right )+65536\right ) \ln \left (x \right )}\)	\(415\)

Fricas [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (20) = 40\).

Time = 0.29 (sec) , antiderivative size = 77, normalized size of antiderivative = 3.67 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {{\left (e^{4} + 2\right )} \log \left (2\right )^{4} + 64 \, {\left (e^{4} + 2\right )} \log \left (2\right )^{3} + 1536 \, {\left (e^{4} + 2\right )} \log \left (2\right )^{2} + 2 \, x^{2} + 16384 \, {\left (e^{4} + 2\right )} \log \left (2\right ) + 65536 \, e^{4} + 131072}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} \]

Sympy [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (19) = 38\).

Time = 0.07 (sec) , antiderivative size = 102, normalized size of antiderivative = 4.86 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {2 x^{2} + 2 \log {\left (2 \right )}^{4} + e^{4} \log {\left (2 \right )}^{4} + 128 \log {\left (2 \right )}^{3} + 64 e^{4} \log {\left (2 \right )}^{3} + 3072 \log {\left (2 \right )}^{2} + 32768 \log {\left (2 \right )} + 1536 e^{4} \log {\left (2 \right )}^{2} + 131072 + 16384 e^{4} \log {\left (2 \right )} + 65536 e^{4}}{\left (\log {\left (2 \right )}^{4} + 64 \log {\left (2 \right )}^{3} + 1536 \log {\left (2 \right )}^{2} + 16384 \log {\left (2 \right )} + 65536\right ) \log {\left (x \right )}} \]

Maxima [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 371 vs. \(2 (20) = 40\).

Time = 0.33 (sec) , antiderivative size = 371, normalized size of antiderivative = 17.67 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {e^{4} \log \left (2\right )^{4}}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {64 \, e^{4} \log \left (2\right )^{3}}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {2 \, \log \left (2\right )^{4}}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {1536 \, e^{4} \log \left (2\right )^{2}}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {128 \, \log \left (2\right )^{3}}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {2 \, x^{2}}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {16384 \, e^{4} \log \left (2\right )}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {3072 \, \log \left (2\right )^{2}}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {65536 \, e^{4}}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {32768 \, \log \left (2\right )}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} + \frac {131072}{{\left (\log \left (2\right )^{4} + 64 \, \log \left (2\right )^{3} + 1536 \, \log \left (2\right )^{2} + 16384 \, \log \left (2\right ) + 65536\right )} \log \left (x\right )} \]

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (20) = 40\).

Time = 0.26 (sec) , antiderivative size = 99, normalized size of antiderivative = 4.71 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {e^{4} \log \left (2\right )^{4} + 64 \, e^{4} \log \left (2\right )^{3} + 2 \, \log \left (2\right )^{4} + 1536 \, e^{4} \log \left (2\right )^{2} + 128 \, \log \left (2\right )^{3} + 2 \, x^{2} + 16384 \, e^{4} \log \left (2\right ) + 3072 \, \log \left (2\right )^{2} + 65536 \, e^{4} + 32768 \, \log \left (2\right ) + 131072}{\log \left (2\right )^{4} \log \left (x\right ) + 64 \, \log \left (2\right )^{3} \log \left (x\right ) + 1536 \, \log \left (2\right )^{2} \log \left (x\right ) + 16384 \, \log \left (2\right ) \log \left (x\right ) + 65536 \, \log \left (x\right )} \]

Mupad [B] (veriﬁcation not implemented)

Time = 9.86 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.48 \[ \int \frac {-131072-65536 e^4-2 x^2+\left (-32768-16384 e^4\right ) \log (2)+\left (-3072-1536 e^4\right ) \log ^2(2)+\left (-128-64 e^4\right ) \log ^3(2)+\left (-2-e^4\right ) \log ^4(2)+4 x^2 \log (x)}{\left (65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)\right ) \log ^2(x)} \, dx=\frac {2\,x^2+65536\,{\mathrm {e}}^4+32768\,\ln \left (2\right )+16384\,{\mathrm {e}}^4\,\ln \left (2\right )+1536\,{\mathrm {e}}^4\,{\ln \left (2\right )}^2+64\,{\mathrm {e}}^4\,{\ln \left (2\right )}^3+{\mathrm {e}}^4\,{\ln \left (2\right )}^4+3072\,{\ln \left (2\right )}^2+128\,{\ln \left (2\right )}^3+2\,{\ln \left (2\right )}^4+131072}{\ln \left (x\right )\,{\left (\ln \left (2\right )+16\right )}^4} \]

\(\int \frac {-131072-65536 e^4-2 x^2+(-32768-16384 e^4) \log (2)+(-3072-1536 e^4) \log ^2(2)+(-128-64 e^4) \log ^3(2)+(-2-e^4) \log ^4(2)+4 x^2 \log (x)}{(65536 x+16384 x \log (2)+1536 x \log ^2(2)+64 x \log ^3(2)+x \log ^4(2)) \log ^2(x)} \, dx\) [3106]

Optimal result