\(\int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+(-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)) \log (4)+(-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)) \log ^2(4)+(-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)) \log ^3(4)+(-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)) \log ^4(4)}{x^{21} \log ^4(4)} \, dx\) [2878]

Optimal result

Integrand size = 146, antiderivative size = 20 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {(-3+\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \]

[Out]

1/16*(4+2*ln(2))^4*(ln(2)-3)^4/x^20/ln(2)^4

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {12, 30} \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {(3-\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \]

[In]

Int[(-414720 + 552960*Log[2] - 276480*Log[2]^2 + 61440*Log[2]^3 - 5120*Log[2]^4 + (-414720 + 552960*Log[2] - 2
76480*Log[2]^2 + 61440*Log[2]^3 - 5120*Log[2]^4)*Log[4] + (-155520 + 207360*Log[2] - 103680*Log[2]^2 + 23040*L
og[2]^3 - 1920*Log[2]^4)*Log[4]^2 + (-25920 + 34560*Log[2] - 17280*Log[2]^2 + 3840*Log[2]^3 - 320*Log[2]^4)*Lo
g[4]^3 + (-1620 + 2160*Log[2] - 1080*Log[2]^2 + 240*Log[2]^3 - 20*Log[2]^4)*Log[4]^4)/(x^21*Log[4]^4),x]

[Out]

((3 - Log[2])^4*(4 + Log[4])^4)/(x^20*Log[4]^4)

Rule 12

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

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps \begin{align*} \text {integral}& = -\frac {\left (20 (3-\log (2))^4 (4+\log (4))^4\right ) \int \frac {1}{x^{21}} \, dx}{\log ^4(4)} \\ & = \frac {(3-\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {(-3+\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \]

[In]

Integrate[(-414720 + 552960*Log[2] - 276480*Log[2]^2 + 61440*Log[2]^3 - 5120*Log[2]^4 + (-414720 + 552960*Log[
2] - 276480*Log[2]^2 + 61440*Log[2]^3 - 5120*Log[2]^4)*Log[4] + (-155520 + 207360*Log[2] - 103680*Log[2]^2 + 2
3040*Log[2]^3 - 1920*Log[2]^4)*Log[4]^2 + (-25920 + 34560*Log[2] - 17280*Log[2]^2 + 3840*Log[2]^3 - 320*Log[2]
^4)*Log[4]^3 + (-1620 + 2160*Log[2] - 1080*Log[2]^2 + 240*Log[2]^3 - 20*Log[2]^4)*Log[4]^4)/(x^21*Log[4]^4),x]

[Out]

((-3 + Log[2])^4*(4 + Log[4])^4)/(x^20*Log[4]^4)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(54\) vs. \(2(23)=46\).

Time = 0.10 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.75

method	result	size
gosper	\(\frac {\ln \left (2\right )^{8}-4 \ln \left (2\right )^{7}-18 \ln \left (2\right )^{6}+68 \ln \left (2\right )^{5}+145 \ln \left (2\right )^{4}-408 \ln \left (2\right )^{3}-648 \ln \left (2\right )^{2}+864 \ln \left (2\right )+1296}{x^{20} \ln \left (2\right )^{4}}\)	\(55\)
norman	\(\frac {\ln \left (2\right )^{8}-4 \ln \left (2\right )^{7}-18 \ln \left (2\right )^{6}+68 \ln \left (2\right )^{5}+145 \ln \left (2\right )^{4}-408 \ln \left (2\right )^{3}-648 \ln \left (2\right )^{2}+864 \ln \left (2\right )+1296}{x^{20} \ln \left (2\right )^{4}}\)	\(55\)
risch	\(\frac {\ln \left (2\right )^{4}}{x^{20}}-\frac {4 \ln \left (2\right )^{3}}{x^{20}}-\frac {18 \ln \left (2\right )^{2}}{x^{20}}+\frac {68 \ln \left (2\right )}{x^{20}}+\frac {145}{x^{20}}-\frac {408}{x^{20} \ln \left (2\right )}-\frac {648}{x^{20} \ln \left (2\right )^{2}}+\frac {864}{x^{20} \ln \left (2\right )^{3}}+\frac {1296}{x^{20} \ln \left (2\right )^{4}}\)	\(76\)
default	\(-\frac {8 \left (-20 \ln \left (2\right )^{4}+240 \ln \left (2\right )^{3}-1080 \ln \left (2\right )^{2}+2160 \ln \left (2\right )-1620\right ) \ln \left (2\right )^{4}+4 \left (-320 \ln \left (2\right )^{4}+3840 \ln \left (2\right )^{3}-17280 \ln \left (2\right )^{2}+34560 \ln \left (2\right )-25920\right ) \ln \left (2\right )^{3}+2 \left (-1920 \ln \left (2\right )^{4}+23040 \ln \left (2\right )^{3}-103680 \ln \left (2\right )^{2}+207360 \ln \left (2\right )-155520\right ) \ln \left (2\right )^{2}+\left (-5120 \ln \left (2\right )^{4}+61440 \ln \left (2\right )^{3}-276480 \ln \left (2\right )^{2}+552960 \ln \left (2\right )-414720\right ) \ln \left (2\right )-2560 \ln \left (2\right )^{4}+30720 \ln \left (2\right )^{3}-138240 \ln \left (2\right )^{2}+276480 \ln \left (2\right )-207360}{160 \ln \left (2\right )^{4} x^{20}}\)	\(151\)
parallelrisch	\(-\frac {16 \left (-20 \ln \left (2\right )^{4}+240 \ln \left (2\right )^{3}-1080 \ln \left (2\right )^{2}+2160 \ln \left (2\right )-1620\right ) \ln \left (2\right )^{4}+8 \left (-320 \ln \left (2\right )^{4}+3840 \ln \left (2\right )^{3}-17280 \ln \left (2\right )^{2}+34560 \ln \left (2\right )-25920\right ) \ln \left (2\right )^{3}+4 \left (-1920 \ln \left (2\right )^{4}+23040 \ln \left (2\right )^{3}-103680 \ln \left (2\right )^{2}+207360 \ln \left (2\right )-155520\right ) \ln \left (2\right )^{2}+2 \left (-5120 \ln \left (2\right )^{4}+61440 \ln \left (2\right )^{3}-276480 \ln \left (2\right )^{2}+552960 \ln \left (2\right )-414720\right ) \ln \left (2\right )-5120 \ln \left (2\right )^{4}+61440 \ln \left (2\right )^{3}-276480 \ln \left (2\right )^{2}+552960 \ln \left (2\right )-414720}{320 x^{20} \ln \left (2\right )^{4}}\)	\(152\)

[In]

int(1/16*(16*(-20*ln(2)^4+240*ln(2)^3-1080*ln(2)^2+2160*ln(2)-1620)*ln(2)^4+8*(-320*ln(2)^4+3840*ln(2)^3-17280
*ln(2)^2+34560*ln(2)-25920)*ln(2)^3+4*(-1920*ln(2)^4+23040*ln(2)^3-103680*ln(2)^2+207360*ln(2)-155520)*ln(2)^2
+2*(-5120*ln(2)^4+61440*ln(2)^3-276480*ln(2)^2+552960*ln(2)-414720)*ln(2)-5120*ln(2)^4+61440*ln(2)^3-276480*ln
(2)^2+552960*ln(2)-414720)/x^21/ln(2)^4,x,method=_RETURNVERBOSE)

[Out]

(ln(2)^8-4*ln(2)^7-18*ln(2)^6+68*ln(2)^5+145*ln(2)^4-408*ln(2)^3-648*ln(2)^2+864*ln(2)+1296)/x^20/ln(2)^4

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (20) = 40\).

Time = 0.22 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.70 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {\log \left (2\right )^{8} - 4 \, \log \left (2\right )^{7} - 18 \, \log \left (2\right )^{6} + 68 \, \log \left (2\right )^{5} + 145 \, \log \left (2\right )^{4} - 408 \, \log \left (2\right )^{3} - 648 \, \log \left (2\right )^{2} + 864 \, \log \left (2\right ) + 1296}{x^{20} \log \left (2\right )^{4}} \]

[In]

integrate(1/16*(16*(-20*log(2)^4+240*log(2)^3-1080*log(2)^2+2160*log(2)-1620)*log(2)^4+8*(-320*log(2)^4+3840*l
og(2)^3-17280*log(2)^2+34560*log(2)-25920)*log(2)^3+4*(-1920*log(2)^4+23040*log(2)^3-103680*log(2)^2+207360*lo
g(2)-155520)*log(2)^2+2*(-5120*log(2)^4+61440*log(2)^3-276480*log(2)^2+552960*log(2)-414720)*log(2)-5120*log(2
)^4+61440*log(2)^3-276480*log(2)^2+552960*log(2)-414720)/x^21/log(2)^4,x, algorithm="fricas")

[Out]

(log(2)^8 - 4*log(2)^7 - 18*log(2)^6 + 68*log(2)^5 + 145*log(2)^4 - 408*log(2)^3 - 648*log(2)^2 + 864*log(2) +
1296)/(x^20*log(2)^4)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (24) = 48\).

Time = 0.06 (sec) , antiderivative size = 65, normalized size of antiderivative = 3.25 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=- \frac {-25920 - 17280 \log {\left (2 \right )} - 2900 \log {\left (2 \right )}^{4} - 1360 \log {\left (2 \right )}^{5} - 20 \log {\left (2 \right )}^{8} + 80 \log {\left (2 \right )}^{7} + 360 \log {\left (2 \right )}^{6} + 8160 \log {\left (2 \right )}^{3} + 12960 \log {\left (2 \right )}^{2}}{20 x^{20} \log {\left (2 \right )}^{4}} \]

[In]

integrate(1/16*(16*(-20*ln(2)**4+240*ln(2)**3-1080*ln(2)**2+2160*ln(2)-1620)*ln(2)**4+8*(-320*ln(2)**4+3840*ln
(2)**3-17280*ln(2)**2+34560*ln(2)-25920)*ln(2)**3+4*(-1920*ln(2)**4+23040*ln(2)**3-103680*ln(2)**2+207360*ln(2
)-155520)*ln(2)**2+2*(-5120*ln(2)**4+61440*ln(2)**3-276480*ln(2)**2+552960*ln(2)-414720)*ln(2)-5120*ln(2)**4+6
1440*ln(2)**3-276480*ln(2)**2+552960*ln(2)-414720)/x**21/ln(2)**4,x)

[Out]

-(-25920 - 17280*log(2) - 2900*log(2)**4 - 1360*log(2)**5 - 20*log(2)**8 + 80*log(2)**7 + 360*log(2)**6 + 8160
*log(2)**3 + 12960*log(2)**2)/(20*x**20*log(2)**4)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (20) = 40\).

Time = 0.22 (sec) , antiderivative size = 141, normalized size of antiderivative = 7.05 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {{\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{4} + 8 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{3} + 16 \, \log \left (2\right )^{4} + 24 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{2} - 192 \, \log \left (2\right )^{3} + 32 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right ) + 864 \, \log \left (2\right )^{2} - 1728 \, \log \left (2\right ) + 1296}{x^{20} \log \left (2\right )^{4}} \]

[In]

integrate(1/16*(16*(-20*log(2)^4+240*log(2)^3-1080*log(2)^2+2160*log(2)-1620)*log(2)^4+8*(-320*log(2)^4+3840*l
og(2)^3-17280*log(2)^2+34560*log(2)-25920)*log(2)^3+4*(-1920*log(2)^4+23040*log(2)^3-103680*log(2)^2+207360*lo
g(2)-155520)*log(2)^2+2*(-5120*log(2)^4+61440*log(2)^3-276480*log(2)^2+552960*log(2)-414720)*log(2)-5120*log(2
)^4+61440*log(2)^3-276480*log(2)^2+552960*log(2)-414720)/x^21/log(2)^4,x, algorithm="maxima")

[Out]

((log(2)^4 - 12*log(2)^3 + 54*log(2)^2 - 108*log(2) + 81)*log(2)^4 + 8*(log(2)^4 - 12*log(2)^3 + 54*log(2)^2 -
108*log(2) + 81)*log(2)^3 + 16*log(2)^4 + 24*(log(2)^4 - 12*log(2)^3 + 54*log(2)^2 - 108*log(2) + 81)*log(2)^
2 - 192*log(2)^3 + 32*(log(2)^4 - 12*log(2)^3 + 54*log(2)^2 - 108*log(2) + 81)*log(2) + 864*log(2)^2 - 1728*lo
g(2) + 1296)/(x^20*log(2)^4)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (20) = 40\).

Time = 0.26 (sec) , antiderivative size = 141, normalized size of antiderivative = 7.05 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {{\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{4} + 8 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{3} + 16 \, \log \left (2\right )^{4} + 24 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{2} - 192 \, \log \left (2\right )^{3} + 32 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right ) + 864 \, \log \left (2\right )^{2} - 1728 \, \log \left (2\right ) + 1296}{x^{20} \log \left (2\right )^{4}} \]

[In]

integrate(1/16*(16*(-20*log(2)^4+240*log(2)^3-1080*log(2)^2+2160*log(2)-1620)*log(2)^4+8*(-320*log(2)^4+3840*l
og(2)^3-17280*log(2)^2+34560*log(2)-25920)*log(2)^3+4*(-1920*log(2)^4+23040*log(2)^3-103680*log(2)^2+207360*lo
g(2)-155520)*log(2)^2+2*(-5120*log(2)^4+61440*log(2)^3-276480*log(2)^2+552960*log(2)-414720)*log(2)-5120*log(2
)^4+61440*log(2)^3-276480*log(2)^2+552960*log(2)-414720)/x^21/log(2)^4,x, algorithm="giac")

[Out]

((log(2)^4 - 12*log(2)^3 + 54*log(2)^2 - 108*log(2) + 81)*log(2)^4 + 8*(log(2)^4 - 12*log(2)^3 + 54*log(2)^2 -
108*log(2) + 81)*log(2)^3 + 16*log(2)^4 + 24*(log(2)^4 - 12*log(2)^3 + 54*log(2)^2 - 108*log(2) + 81)*log(2)^
2 - 192*log(2)^3 + 32*(log(2)^4 - 12*log(2)^3 + 54*log(2)^2 - 108*log(2) + 81)*log(2) + 864*log(2)^2 - 1728*lo
g(2) + 1296)/(x^20*log(2)^4)

Mupad [B] (verification not implemented)

Time = 9.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {{\left (\ln \left (2\right )-{\ln \left (2\right )}^2+6\right )}^4}{x^{20}\,{\ln \left (2\right )}^4} \]

[In]

int(-((log(2)*(276480*log(2)^2 - 552960*log(2) - 61440*log(2)^3 + 5120*log(2)^4 + 414720))/8 - 34560*log(2) +
17280*log(2)^2 - 3840*log(2)^3 + 320*log(2)^4 + log(2)^4*(1080*log(2)^2 - 2160*log(2) - 240*log(2)^3 + 20*log(
2)^4 + 1620) + (log(2)^3*(17280*log(2)^2 - 34560*log(2) - 3840*log(2)^3 + 320*log(2)^4 + 25920))/2 + (log(2)^2
*(103680*log(2)^2 - 207360*log(2) - 23040*log(2)^3 + 1920*log(2)^4 + 155520))/4 + 25920)/(x^21*log(2)^4),x)

[Out]

(log(2) - log(2)^2 + 6)^4/(x^20*log(2)^4)