Optimal. Leaf size=23 \[ \frac {(-4-\log (3+i \pi -x+\log (3)))^2}{x^4} \]
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Rubi [C] time = 1.97, antiderivative size = 511, normalized size of antiderivative = 22.22, number of steps used = 44, number of rules used = 24, integrand size = 101, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.238, Rules used = {6, 1593, 6741, 6742, 77, 2418, 2395, 44, 2394, 2315, 2390, 12, 2301, 36, 29, 31, 2398, 2411, 2347, 2344, 2317, 2391, 2314, 2319} \begin {gather*} -\frac {2 \text {Li}_2\left (1-\frac {x}{3+i \pi +\log (3)}\right )}{(\pi -i (3+\log (3)))^4}+\frac {2 \text {Li}_2\left (1-\frac {x}{3+i \pi +\log (3)}\right )}{(3+i \pi +\log (3))^4}+\frac {16}{x^4}+\frac {\log ^2(-x+i \pi +3+\log (3))}{x^4}+\frac {8 \log (-x+i \pi +3+\log (3))}{x^4}-\frac {\log (-x+i \pi +3+\log (3))}{x^2 (\pi -i (3+\log (3)))^2}-\frac {\log (-x+i \pi +3+\log (3))}{x^2 (3+i \pi +\log (3))^2}+\frac {1}{3 x^2 (\pi -i (3+\log (3)))^2}+\frac {1}{3 x^2 (3+i \pi +\log (3))^2}+\frac {\log ^2(-x+i \pi +3+\log (3))}{(\pi -i (3+\log (3)))^4}-\frac {\log ^2(-x+i \pi +3+\log (3))}{(3+i \pi +\log (3))^4}-\frac {2 (-x+i \pi +3+\log (3)) \log (-x+i \pi +3+\log (3))}{x (3+i \pi +\log (3))^4}-\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (-x+i \pi +3+\log (3))}{(\pi -i (3+\log (3)))^4}+\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (-x+i \pi +3+\log (3))}{(3+i \pi +\log (3))^4}+\frac {2 \log (-x+i \pi +3+\log (3))}{x (3+i \pi +\log (3))^3}+\frac {11 \log (x)}{3 (\pi -i (3+\log (3)))^4}-\frac {11 \log (x)}{3 (3+i \pi +\log (3))^4}-\frac {11 \log (-i x-\pi +i (3+\log (3)))}{3 (\pi -i (3+\log (3)))^4}+\frac {5 \log (-i x-\pi +i (3+\log (3)))}{3 (3+i \pi +\log (3))^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 29
Rule 31
Rule 36
Rule 44
Rule 77
Rule 1593
Rule 2301
Rule 2314
Rule 2315
Rule 2317
Rule 2319
Rule 2344
Rule 2347
Rule 2390
Rule 2391
Rule 2394
Rule 2395
Rule 2398
Rule 2411
Rule 2418
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-192+56 x-64 (i \pi +\log (3))+(-96+30 x-32 (i \pi +\log (3))) \log (3+i \pi -x+\log (3))+(-12+4 x-4 (i \pi +\log (3))) \log ^2(3+i \pi -x+\log (3))}{-x^6+x^5 (3+i \pi +\log (3))} \, dx\\ &=\int \frac {-192+56 x-64 (i \pi +\log (3))+(-96+30 x-32 (i \pi +\log (3))) \log (3+i \pi -x+\log (3))+(-12+4 x-4 (i \pi +\log (3))) \log ^2(3+i \pi -x+\log (3))}{x^5 (3+i \pi -x+\log (3))} \, dx\\ &=\int \frac {56 x-192 \left (1+\frac {1}{3} (i \pi +\log (3))\right )+(-96+30 x-32 (i \pi +\log (3))) \log (3+i \pi -x+\log (3))+(-12+4 x-4 (i \pi +\log (3))) \log ^2(3+i \pi -x+\log (3))}{x^5 (3+i \pi -x+\log (3))} \, dx\\ &=\int \left (-\frac {8 (-24-8 i \pi +7 x-8 \log (3))}{x^5 (-3-i \pi +x-\log (3))}-\frac {2 (-48-16 i \pi +15 x-16 \log (3)) \log (3+i \pi -x+\log (3))}{x^5 (-3-i \pi +x-\log (3))}-\frac {4 \log ^2(3+i \pi -x+\log (3))}{x^5}\right ) \, dx\\ &=-\left (2 \int \frac {(-48-16 i \pi +15 x-16 \log (3)) \log (3+i \pi -x+\log (3))}{x^5 (-3-i \pi +x-\log (3))} \, dx\right )-4 \int \frac {\log ^2(3+i \pi -x+\log (3))}{x^5} \, dx-8 \int \frac {-24-8 i \pi +7 x-8 \log (3)}{x^5 (-3-i \pi +x-\log (3))} \, dx\\ &=\frac {\log ^2(3+i \pi -x+\log (3))}{x^4}+2 \int \frac {\log (3+i \pi -x+\log (3))}{x^4 (3+i \pi -x+\log (3))} \, dx-2 \int \left (\frac {16 \log (3+i \pi -x+\log (3))}{x^5}+\frac {\log (3+i \pi -x+\log (3))}{x (\pi -i (3+\log (3)))^4}-\frac {i \log (3+i \pi -x+\log (3))}{(-3 i+\pi +i x-i \log (3)) (\pi -i (3+\log (3)))^4}+\frac {i \log (3+i \pi -x+\log (3))}{x^2 (\pi -i (3+\log (3)))^3}-\frac {\log (3+i \pi -x+\log (3))}{x^3 (\pi -i (3+\log (3)))^2}-\frac {i \log (3+i \pi -x+\log (3))}{x^4 (\pi -i (3+\log (3)))}\right ) \, dx-8 \int \left (\frac {8}{x^5}+\frac {1}{x (\pi -i (3+\log (3)))^4}-\frac {i}{(-3 i+\pi +i x-i \log (3)) (\pi -i (3+\log (3)))^4}+\frac {i}{x^2 (\pi -i (3+\log (3)))^3}-\frac {1}{x^3 (\pi -i (3+\log (3)))^2}-\frac {i}{x^4 (\pi -i (3+\log (3)))}\right ) \, dx\\ &=\frac {16}{x^4}+\frac {8}{x (3+i \pi +\log (3))^3}+\frac {8}{3 x^3 (3+i \pi +\log (3))}-\frac {4}{x^2 (\pi -i (3+\log (3)))^2}-\frac {8 \log (x)}{(\pi -i (3+\log (3)))^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{x^4}+\frac {8 \log (-\pi -i x+i (3+\log (3)))}{(\pi -i (3+\log (3)))^4}-2 \operatorname {Subst}\left (\int \frac {\log (x)}{x (3+i \pi -x+\log (3))^4} \, dx,x,3+i \pi -x+\log (3)\right )-32 \int \frac {\log (3+i \pi -x+\log (3))}{x^5} \, dx-\frac {2 \int \frac {\log (3+i \pi -x+\log (3))}{x^2} \, dx}{(3+i \pi +\log (3))^3}-\frac {2 \int \frac {\log (3+i \pi -x+\log (3))}{x^4} \, dx}{3+i \pi +\log (3)}+\frac {(2 i) \int \frac {\log (3+i \pi -x+\log (3))}{-3 i+\pi +i x-i \log (3)} \, dx}{(\pi -i (3+\log (3)))^4}-\frac {2 \int \frac {\log (3+i \pi -x+\log (3))}{x} \, dx}{(\pi -i (3+\log (3)))^4}+\frac {2 \int \frac {\log (3+i \pi -x+\log (3))}{x^3} \, dx}{(\pi -i (3+\log (3)))^2}\\ &=\frac {16}{x^4}+\frac {8}{x (3+i \pi +\log (3))^3}+\frac {8}{3 x^3 (3+i \pi +\log (3))}-\frac {4}{x^2 (\pi -i (3+\log (3)))^2}-\frac {8 \log (x)}{(\pi -i (3+\log (3)))^4}+\frac {8 \log (3+i \pi -x+\log (3))}{x^4}+\frac {2 \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^3}+\frac {2 \log (3+i \pi -x+\log (3))}{3 x^3 (3+i \pi +\log (3))}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (\pi -i (3+\log (3)))^2}-\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{x^4}+\frac {8 \log (-\pi -i x+i (3+\log (3)))}{(\pi -i (3+\log (3)))^4}+8 \int \frac {1}{x^4 (3+i \pi -x+\log (3))} \, dx+\frac {2 \int \frac {1}{x (3+i \pi -x+\log (3))} \, dx}{(3+i \pi +\log (3))^3}+\frac {2 \int \frac {1}{x^3 (3+i \pi -x+\log (3))} \, dx}{3 (3+i \pi +\log (3))}-\frac {2 \operatorname {Subst}\left (\int \frac {\log (x)}{(3+i \pi -x+\log (3))^4} \, dx,x,3+i \pi -x+\log (3)\right )}{3+i \pi +\log (3)}-\frac {2 \operatorname {Subst}\left (\int \frac {\log (x)}{x (3+i \pi -x+\log (3))^3} \, dx,x,3+i \pi -x+\log (3)\right )}{3+i \pi +\log (3)}-\frac {(2 i) \operatorname {Subst}\left (\int \frac {(3+i \pi +\log (3)) \log (x)}{x (-3 i+\pi -i \log (3))} \, dx,x,3+i \pi -x+\log (3)\right )}{(\pi -i (3+\log (3)))^4}-\frac {2 \int \frac {\log \left (-\frac {x}{-3-i \pi -\log (3)}\right )}{3+i \pi -x+\log (3)} \, dx}{(\pi -i (3+\log (3)))^4}-\frac {\int \frac {1}{x^2 (3+i \pi -x+\log (3))} \, dx}{(\pi -i (3+\log (3)))^2}\\ &=\frac {16}{x^4}+\frac {8}{x (3+i \pi +\log (3))^3}+\frac {8}{3 x^3 (3+i \pi +\log (3))}-\frac {4}{x^2 (\pi -i (3+\log (3)))^2}-\frac {8 \log (x)}{(\pi -i (3+\log (3)))^4}+\frac {8 \log (3+i \pi -x+\log (3))}{x^4}+\frac {2 \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^3}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (\pi -i (3+\log (3)))^2}-\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{x^4}+\frac {8 \log (-\pi -i x+i (3+\log (3)))}{(\pi -i (3+\log (3)))^4}-\frac {2 \text {Li}_2\left (1-\frac {x}{3+i \pi +\log (3)}\right )}{(\pi -i (3+\log (3)))^4}+8 \int \left (\frac {1}{x (\pi -i (3+\log (3)))^4}-\frac {i}{(-3 i+\pi +i x-i \log (3)) (\pi -i (3+\log (3)))^4}+\frac {i}{x^2 (\pi -i (3+\log (3)))^3}-\frac {1}{x^3 (\pi -i (3+\log (3)))^2}-\frac {i}{x^4 (\pi -i (3+\log (3)))}\right ) \, dx+\frac {2 \int \frac {1}{x} \, dx}{(3+i \pi +\log (3))^4}+\frac {2 \int \frac {1}{3+i \pi -x+\log (3)} \, dx}{(3+i \pi +\log (3))^4}-\frac {2 \operatorname {Subst}\left (\int \frac {\log (x)}{(3+i \pi -x+\log (3))^3} \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^2}-\frac {2 \operatorname {Subst}\left (\int \frac {\log (x)}{x (3+i \pi -x+\log (3))^2} \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^2}+\frac {2 \int \left (\frac {i}{x (\pi -i (3+\log (3)))^3}+\frac {1}{(-3 i+\pi +i x-i \log (3)) (\pi -i (3+\log (3)))^3}-\frac {1}{x^2 (\pi -i (3+\log (3)))^2}-\frac {i}{x^3 (\pi -i (3+\log (3)))}\right ) \, dx}{3 (3+i \pi +\log (3))}+\frac {2 \operatorname {Subst}\left (\int \frac {1}{x (3+i \pi -x+\log (3))^3} \, dx,x,3+i \pi -x+\log (3)\right )}{3 (3+i \pi +\log (3))}+\frac {2 \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,3+i \pi -x+\log (3)\right )}{(\pi -i (3+\log (3)))^4}-\frac {\int \left (-\frac {1}{x (\pi -i (3+\log (3)))^2}+\frac {i}{(-3 i+\pi +i x-i \log (3)) (\pi -i (3+\log (3)))^2}-\frac {i}{x^2 (\pi -i (3+\log (3)))}\right ) \, dx}{(\pi -i (3+\log (3)))^2}\\ &=\frac {16}{x^4}-\frac {5}{3 x (3+i \pi +\log (3))^3}-\frac {1}{3 x^2 (3+i \pi +\log (3))^2}+\frac {8 \log (x)}{3 (3+i \pi +\log (3))^4}+\frac {\log (x)}{(\pi -i (3+\log (3)))^4}+\frac {8 \log (3+i \pi -x+\log (3))}{x^4}+\frac {2 \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^3}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (3+i \pi +\log (3))^2}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (\pi -i (3+\log (3)))^2}-\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{x^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}-\frac {8 \log (-\pi -i x+i (3+\log (3)))}{3 (3+i \pi +\log (3))^4}-\frac {\log (-\pi -i x+i (3+\log (3)))}{(\pi -i (3+\log (3)))^4}-\frac {2 \text {Li}_2\left (1-\frac {x}{3+i \pi +\log (3)}\right )}{(\pi -i (3+\log (3)))^4}-\frac {2 \operatorname {Subst}\left (\int \frac {\log (x)}{(3+i \pi -x+\log (3))^2} \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^3}-\frac {2 \operatorname {Subst}\left (\int \frac {\log (x)}{x (3+i \pi -x+\log (3))} \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^3}+\frac {\operatorname {Subst}\left (\int \frac {1}{x (3+i \pi -x+\log (3))^2} \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^2}+\frac {2 \operatorname {Subst}\left (\int \left (\frac {i}{x (\pi -i (3+\log (3)))^3}+\frac {1}{(-3 i+\pi +i x-i \log (3)) (\pi -i (3+\log (3)))^3}+\frac {1}{(3 i-\pi -i x+i \log (3))^2 (\pi -i (3+\log (3)))^2}+\frac {1}{(-3 i+\pi +i x-i \log (3))^3 (\pi -i (3+\log (3)))}\right ) \, dx,x,3+i \pi -x+\log (3)\right )}{3 (3+i \pi +\log (3))}\\ &=\frac {16}{x^4}-\frac {1}{x (3+i \pi +\log (3))^3}+\frac {2 \log (x)}{(3+i \pi +\log (3))^4}+\frac {\log (x)}{(\pi -i (3+\log (3)))^4}+\frac {8 \log (3+i \pi -x+\log (3))}{x^4}+\frac {2 \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^3}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (3+i \pi +\log (3))^2}-\frac {2 (3+i \pi -x+\log (3)) \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^4}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (\pi -i (3+\log (3)))^2}-\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{x^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}-\frac {2 \log (-\pi -i x+i (3+\log (3)))}{(3+i \pi +\log (3))^4}-\frac {\log (-\pi -i x+i (3+\log (3)))}{(\pi -i (3+\log (3)))^4}-\frac {2 \text {Li}_2\left (1-\frac {x}{3+i \pi +\log (3)}\right )}{(\pi -i (3+\log (3)))^4}+\frac {2 \operatorname {Subst}\left (\int \frac {1}{3+i \pi -x+\log (3)} \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^4}-\frac {2 \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^4}-\frac {2 \operatorname {Subst}\left (\int \frac {\log (x)}{3+i \pi -x+\log (3)} \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^4}+\frac {\operatorname {Subst}\left (\int \left (-\frac {1}{x (\pi -i (3+\log (3)))^2}+\frac {i}{(-3 i+\pi +i x-i \log (3)) (\pi -i (3+\log (3)))^2}+\frac {i}{(3 i-\pi -i x+i \log (3))^2 (\pi -i (3+\log (3)))}\right ) \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^2}\\ &=\frac {16}{x^4}+\frac {8 \log (3+i \pi -x+\log (3))}{x^4}+\frac {2 \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^3}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (3+i \pi +\log (3))^2}-\frac {2 (3+i \pi -x+\log (3)) \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^4}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (\pi -i (3+\log (3)))^2}+\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (3+i \pi -x+\log (3))}{(3+i \pi +\log (3))^4}-\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{x^4}-\frac {\log ^2(3+i \pi -x+\log (3))}{(3+i \pi +\log (3))^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}-\frac {2 \log (-\pi -i x+i (3+\log (3)))}{(3+i \pi +\log (3))^4}-\frac {2 \text {Li}_2\left (1-\frac {x}{3+i \pi +\log (3)}\right )}{(\pi -i (3+\log (3)))^4}-\frac {2 \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {x}{3+i \pi +\log (3)}\right )}{x} \, dx,x,3+i \pi -x+\log (3)\right )}{(3+i \pi +\log (3))^4}\\ &=\frac {16}{x^4}+\frac {8 \log (3+i \pi -x+\log (3))}{x^4}+\frac {2 \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^3}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (3+i \pi +\log (3))^2}-\frac {2 (3+i \pi -x+\log (3)) \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^4}-\frac {\log (3+i \pi -x+\log (3))}{x^2 (\pi -i (3+\log (3)))^2}+\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (3+i \pi -x+\log (3))}{(3+i \pi +\log (3))^4}-\frac {2 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{x^4}-\frac {\log ^2(3+i \pi -x+\log (3))}{(3+i \pi +\log (3))^4}+\frac {\log ^2(3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}-\frac {2 \log (-\pi -i x+i (3+\log (3)))}{(3+i \pi +\log (3))^4}+\frac {2 \text {Li}_2\left (1-\frac {x}{3+i \pi +\log (3)}\right )}{(3+i \pi +\log (3))^4}-\frac {2 \text {Li}_2\left (1-\frac {x}{3+i \pi +\log (3)}\right )}{(\pi -i (3+\log (3)))^4}\\ \end {aligned} \end {gather*}
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Mathematica [C] time = 1.28, size = 917, normalized size = 39.87 \begin {gather*} \frac {1}{6} \left (\frac {96}{x^4}+\frac {12 \log (x)}{(\pi -i (3+\log (3)))^4}-\frac {12 \log (-\pi -i (-3+x-\log (3)))}{(\pi -i (3+\log (3)))^4}+\frac {2 (\pi -i (3+\log (3))) (\pi -i (3+2 x+\log (3)))+4 x^2 \log (x)-4 x^2 \log (-\pi -i (-3+x-\log (3)))}{x^2 (\pi -i (3+\log (3)))^4}+\frac {2 (12+4 i \pi +\log (81)) \left ((\pi -i (3+\log (3))) \left (2 \pi ^2-6 x^2-3 x (3+\log (3))-2 (3+\log (3))^2-i \pi (12+3 x+\log (81))\right )-6 i x^3 \log (x)+6 i x^3 \log (-\pi -i (-3+x-\log (3)))\right )}{x^3 (\pi -i (3+\log (3)))^5}+\frac {12 (4 \pi -i (12+\log (81))) \log (3+i \pi -x+\log (3))}{x^4 (\pi -i (3+\log (3)))}+\frac {3 (2 \pi -i (6+\log (9))) \log ^2(3+i \pi -x+\log (3))}{x^4 (\pi -i (3+\log (3)))}+\frac {12 (4+\log (3+i \pi -x+\log (3)))}{x (3+i \pi +\log (3))^3}+\frac {4 (4+\log (3+i \pi -x+\log (3)))}{x^3 (3+i \pi +\log (3))}-\frac {6 (4+\log (3+i \pi -x+\log (3)))}{x^2 (\pi -i (3+\log (3)))^2}-\frac {12 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) (4+\log (3+i \pi -x+\log (3)))}{(\pi -i (3+\log (3)))^4}+\frac {6 (4+\log (3+i \pi -x+\log (3)))^2}{(\pi -i (3+\log (3)))^4}+\frac {6 (-3-i \pi -\log (3)+x \log (x)-x \log (-\pi -i x+i (3+\log (3))))}{x (\pi -i (3+\log (3)))^4}-\frac {12 \text {Li}_2\left (\frac {3+i \pi -x+\log (3)}{3+i \pi +\log (3)}\right )}{(\pi -i (3+\log (3)))^4}+\frac {(2 \pi -i (6+\log (9))) \left (-\frac {1}{x^2 (3+i \pi +\log (3))^2}-\frac {5 i}{x (\pi -i (3+\log (3)))^3}+\frac {11 \log (x)}{(\pi -i (3+\log (3)))^4}-\frac {2 \log (-\pi -i (-3+x-\log (3)))}{(3+i \pi +\log (3))^4}-\frac {9 \log (-\pi -i (-3+x-\log (3)))}{(\pi -i (3+\log (3)))^4}+\frac {6 \log (3+i \pi -x+\log (3))}{x (3+i \pi +\log (3))^3}+\frac {2 \log (3+i \pi -x+\log (3))}{x^3 (3+i \pi +\log (3))}-\frac {3 \log (3+i \pi -x+\log (3))}{x^2 (\pi -i (3+\log (3)))^2}-\frac {6 \log \left (\frac {x}{3+i \pi +\log (3)}\right ) \log (3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}+\frac {3 \log ^2(3+i \pi -x+\log (3))}{(\pi -i (3+\log (3)))^4}-\frac {6 \text {Li}_2\left (\frac {3+i \pi -x+\log (3)}{3+i \pi +\log (3)}\right )}{(\pi -i (3+\log (3)))^4}\right )}{-\pi +i (3+\log (3))}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 32, normalized size = 1.39 \begin {gather*} \frac {\log \left (i \, \pi - x + \log \relax (3) + 3\right )^{2} + 8 \, \log \left (i \, \pi - x + \log \relax (3) + 3\right ) + 16}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.37, size = 39, normalized size = 1.70 \begin {gather*} \frac {\log \left (i \, \pi - x + \log \relax (3) + 3\right )^{2}}{x^{4}} + \frac {8 \, \log \left (i \, \pi - x + \log \relax (3) + 3\right )}{x^{4}} + \frac {16}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.65, size = 35, normalized size = 1.52
method | result | size |
norman | \(\frac {16+\ln \left (\ln \relax (3)+i \pi +3-x \right )^{2}+8 \ln \left (\ln \relax (3)+i \pi +3-x \right )}{x^{4}}\) | \(35\) |
risch | \(\frac {\ln \left (\ln \relax (3)+i \pi +3-x \right )^{2}}{x^{4}}+\frac {8 \ln \left (\ln \relax (3)+i \pi +3-x \right )}{x^{4}}+\frac {16}{x^{4}}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.92, size = 1585, normalized size = 68.91 result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.67, size = 20, normalized size = 0.87 \begin {gather*} \frac {{\left (\ln \left (\ln \relax (3)-x+3+\Pi \,1{}\mathrm {i}\right )+4\right )}^2}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.87, size = 37, normalized size = 1.61 \begin {gather*} \frac {\log {\left (- x + \log {\relax (3 )} + 3 + i \pi \right )}^{2}}{x^{4}} + \frac {8 \log {\left (- x + \log {\relax (3 )} + 3 + i \pi \right )}}{x^{4}} + \frac {16}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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