Интеграл tan(x)^(42) (dx)

Ответ

  1                                                                                                                                                                                                                                                                                                          
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 |                                  3           7            11            15            19            23            27            31            35            39           5           9            13            17            21            25            29            33            37            41    
 |     42              sin(1)    sin (1)     sin (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1)     sin (1)     sin (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1) 
 |  tan  (x) dx = -1 + ------ - --------- - --------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- + --------- + --------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + -----------
 |                     cos(1)        3           7            11            15            19            23            27            31            35            39           5           9            13            17            21            25            29            33            37            41   
/                               3*cos (1)   7*cos (1)   11*cos  (1)   15*cos  (1)   19*cos  (1)   23*cos  (1)   27*cos  (1)   31*cos  (1)   35*cos  (1)   39*cos  (1)   5*cos (1)   9*cos (1)   13*cos  (1)   17*cos  (1)   21*cos  (1)   25*cos  (1)   29*cos  (1)   33*cos  (1)   37*cos  (1)   41*cos  (1)
0                                                                                                                                                                                                                                                                                                            

$${{166966608033225\,\tan ^{41}1-175528998188775\,\tan ^{39}1+ 185017052144925\,\tan ^{37}1-195589455124635\,\tan ^{35}1+ 207443361495825\,\tan ^{33}1-220826804172975\,\tan ^{31}1+ 236056238943525\,\tan ^{29}1-253541886272675\,\tan ^{27}1+ 273825237174489\,\tan ^{25}1-297636127363575\,\tan ^{23}1+ 325982425207725\,\tan ^{21}1-360296364703275\,\tan ^{19}1+ 402684172315425\,\tan ^{17}1-456375395290815\,\tan ^{15}1+ 526586994566325\,\tan ^{13}1-622330084487475\,\tan ^{11}1+ 760625658818025\,\tan ^91-977947275623175\,\tan ^71+1369126185872445 \,\tan ^51-2281876976454075\,\tan ^31+6845630929362225\,\tan 1 }\over{6845630929362225}}-1$$

Численный ответ

1316550.26714047

Ответ (Неопределённый)

  /                                                                                                                                                                                                                                                                                                            
 |                                    3           7            11            15            19            23            27            31            35            39           5           9            13            17            21            25            29            33            37            41    
 |    42                 sin(x)    sin (x)     sin (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x)     sin (x)     sin (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x) 
 | tan  (x) dx = C - x + ------ - --------- - --------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- + --------- + --------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + -----------
 |                       cos(x)        3           7            11            15            19            23            27            31            35            39           5           9            13            17            21            25            29            33            37            41   
/                                 3*cos (x)   7*cos (x)   11*cos  (x)   15*cos  (x)   19*cos  (x)   23*cos  (x)   27*cos  (x)   31*cos  (x)   35*cos  (x)   39*cos  (x)   5*cos (x)   9*cos (x)   13*cos  (x)   17*cos  (x)   21*cos  (x)   25*cos  (x)   29*cos  (x)   33*cos  (x)   37*cos  (x)   41*cos  (x)

$${{166966608033225\,\tan ^{41}x-175528998188775\,\tan ^{39}x+ 185017052144925\,\tan ^{37}x-195589455124635\,\tan ^{35}x+ 207443361495825\,\tan ^{33}x-220826804172975\,\tan ^{31}x+ 236056238943525\,\tan ^{29}x-253541886272675\,\tan ^{27}x+ 273825237174489\,\tan ^{25}x-297636127363575\,\tan ^{23}x+ 325982425207725\,\tan ^{21}x-360296364703275\,\tan ^{19}x+ 402684172315425\,\tan ^{17}x-456375395290815\,\tan ^{15}x+ 526586994566325\,\tan ^{13}x-622330084487475\,\tan ^{11}x+ 760625658818025\,\tan ^9x-977947275623175\,\tan ^7x+1369126185872445 \,\tan ^5x-2281876976454075\,\tan ^3x+6845630929362225\,\tan x }\over{6845630929362225}}-x$$