Integral de tg^52x dx

Solución

Ha introducido [src]

  1            
  /            
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 |     52      
 |  tan  (x) dx
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/              
0

$$\int\limits_{0}^{1} \tan^{52}{\left(x \right)}\, dx$$

Integral(tan(x)^52, (x, 0, 1))

Respuesta (Indefinida) [src]

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 |                                    5           9            13            17            21            25            29            33            37            41            45            49           3           7            11            15            19            23            27            31            35            39            43            47            51    
 |    52                 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)      sin  (x)      sin  (x)      sin  (x)      sin  (x)      sin  (x) 
 | tan  (x) dx = C + x - ------ - --------- - --------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- + --------- + --------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + -----------
 |                       cos(x)        5           9            13            17            21            25            29            33            37            41            45            49           3           7            11            15            19            23            27            31            35            39            43            47            51   
/                                 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)   45*cos  (x)   49*cos  (x)   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)   43*cos  (x)   47*cos  (x)   51*cos  (x)

$$\int \tan^{52}{\left(x \right)}\, dx = C + x + \frac{\sin^{51}{\left(x \right)}}{51 \cos^{51}{\left(x \right)}} - \frac{\sin^{49}{\left(x \right)}}{49 \cos^{49}{\left(x \right)}} + \frac{\sin^{47}{\left(x \right)}}{47 \cos^{47}{\left(x \right)}} - \frac{\sin^{45}{\left(x \right)}}{45 \cos^{45}{\left(x \right)}} + \frac{\sin^{43}{\left(x \right)}}{43 \cos^{43}{\left(x \right)}} - \frac{\sin^{41}{\left(x \right)}}{41 \cos^{41}{\left(x \right)}} + \frac{\sin^{39}{\left(x \right)}}{39 \cos^{39}{\left(x \right)}} - \frac{\sin^{37}{\left(x \right)}}{37 \cos^{37}{\left(x \right)}} + \frac{\sin^{35}{\left(x \right)}}{35 \cos^{35}{\left(x \right)}} - \frac{\sin^{33}{\left(x \right)}}{33 \cos^{33}{\left(x \right)}} + \frac{\sin^{31}{\left(x \right)}}{31 \cos^{31}{\left(x \right)}} - \frac{\sin^{29}{\left(x \right)}}{29 \cos^{29}{\left(x \right)}} + \frac{\sin^{27}{\left(x \right)}}{27 \cos^{27}{\left(x \right)}} - \frac{\sin^{25}{\left(x \right)}}{25 \cos^{25}{\left(x \right)}} + \frac{\sin^{23}{\left(x \right)}}{23 \cos^{23}{\left(x \right)}} - \frac{\sin^{21}{\left(x \right)}}{21 \cos^{21}{\left(x \right)}} + \frac{\sin^{19}{\left(x \right)}}{19 \cos^{19}{\left(x \right)}} - \frac{\sin^{17}{\left(x \right)}}{17 \cos^{17}{\left(x \right)}} + \frac{\sin^{15}{\left(x \right)}}{15 \cos^{15}{\left(x \right)}} - \frac{\sin^{13}{\left(x \right)}}{13 \cos^{13}{\left(x \right)}} + \frac{\sin^{11}{\left(x \right)}}{11 \cos^{11}{\left(x \right)}} - \frac{\sin^{9}{\left(x \right)}}{9 \cos^{9}{\left(x \right)}} + \frac{\sin^{7}{\left(x \right)}}{7 \cos^{7}{\left(x \right)}} - \frac{\sin^{5}{\left(x \right)}}{5 \cos^{5}{\left(x \right)}} + \frac{\sin^{3}{\left(x \right)}}{3 \cos^{3}{\left(x \right)}} - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$$

Simplificar

Gráfica

Trazar el gráfico f(x)

Respuesta [src]

                 5           9            13            17            21            25            29            33            37            41            45            49           3           7            11            15            19            23            27            31            35            39            43            47            51    
    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)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1) 
1 - ------ - --------- - --------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- + --------- + --------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + -----------
    cos(1)        5           9            13            17            21            25            29            33            37            41            45            49           3           7            11            15            19            23            27            31            35            39            43            47            51   
             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)   45*cos  (1)   49*cos  (1)   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)   43*cos  (1)   47*cos  (1)   51*cos  (1)

$$- \frac{\sin^{49}{\left(1 \right)}}{49 \cos^{49}{\left(1 \right)}} - \frac{\sin^{45}{\left(1 \right)}}{45 \cos^{45}{\left(1 \right)}} - \frac{\sin^{41}{\left(1 \right)}}{41 \cos^{41}{\left(1 \right)}} - \frac{\sin^{37}{\left(1 \right)}}{37 \cos^{37}{\left(1 \right)}} - \frac{\sin^{33}{\left(1 \right)}}{33 \cos^{33}{\left(1 \right)}} - \frac{\sin^{29}{\left(1 \right)}}{29 \cos^{29}{\left(1 \right)}} - \frac{\sin^{25}{\left(1 \right)}}{25 \cos^{25}{\left(1 \right)}} - \frac{\sin^{21}{\left(1 \right)}}{21 \cos^{21}{\left(1 \right)}} - \frac{\sin^{17}{\left(1 \right)}}{17 \cos^{17}{\left(1 \right)}} - \frac{\sin^{13}{\left(1 \right)}}{13 \cos^{13}{\left(1 \right)}} - \frac{\sin^{9}{\left(1 \right)}}{9 \cos^{9}{\left(1 \right)}} - \frac{\sin^{5}{\left(1 \right)}}{5 \cos^{5}{\left(1 \right)}} - \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + 1 + \frac{\sin^{3}{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}} + \frac{\sin^{7}{\left(1 \right)}}{7 \cos^{7}{\left(1 \right)}} + \frac{\sin^{11}{\left(1 \right)}}{11 \cos^{11}{\left(1 \right)}} + \frac{\sin^{15}{\left(1 \right)}}{15 \cos^{15}{\left(1 \right)}} + \frac{\sin^{19}{\left(1 \right)}}{19 \cos^{19}{\left(1 \right)}} + \frac{\sin^{23}{\left(1 \right)}}{23 \cos^{23}{\left(1 \right)}} + \frac{\sin^{27}{\left(1 \right)}}{27 \cos^{27}{\left(1 \right)}} + \frac{\sin^{31}{\left(1 \right)}}{31 \cos^{31}{\left(1 \right)}} + \frac{\sin^{35}{\left(1 \right)}}{35 \cos^{35}{\left(1 \right)}} + \frac{\sin^{39}{\left(1 \right)}}{39 \cos^{39}{\left(1 \right)}} + \frac{\sin^{43}{\left(1 \right)}}{43 \cos^{43}{\left(1 \right)}} + \frac{\sin^{47}{\left(1 \right)}}{47 \cos^{47}{\left(1 \right)}} + \frac{\sin^{51}{\left(1 \right)}}{51 \cos^{51}{\left(1 \right)}}$$

                 5           9            13            17            21            25            29            33            37            41            45            49           3           7            11            15            19            23            27            31            35            39            43            47            51    
    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)      sin  (1)      sin  (1)      sin  (1)      sin  (1)      sin  (1) 
1 - ------ - --------- - --------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- - ----------- + --------- + --------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + ----------- + -----------
    cos(1)        5           9            13            17            21            25            29            33            37            41            45            49           3           7            11            15            19            23            27            31            35            39            43            47            51   
             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)   45*cos  (1)   49*cos  (1)   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)   43*cos  (1)   47*cos  (1)   51*cos  (1)

1 - sin(1)/cos(1) - sin(1)^5/(5*cos(1)^5) - sin(1)^9/(9*cos(1)^9) - sin(1)^13/(13*cos(1)^13) - sin(1)^17/(17*cos(1)^17) - sin(1)^21/(21*cos(1)^21) - sin(1)^25/(25*cos(1)^25) - sin(1)^29/(29*cos(1)^29) - sin(1)^33/(33*cos(1)^33) - sin(1)^37/(37*cos(1)^37) - sin(1)^41/(41*cos(1)^41) - sin(1)^45/(45*cos(1)^45) - sin(1)^49/(49*cos(1)^49) + sin(1)^3/(3*cos(1)^3) + sin(1)^7/(7*cos(1)^7) + sin(1)^11/(11*cos(1)^11) + sin(1)^15/(15*cos(1)^15) + sin(1)^19/(19*cos(1)^19) + sin(1)^23/(23*cos(1)^23) + sin(1)^27/(27*cos(1)^27) + sin(1)^31/(31*cos(1)^31) + sin(1)^35/(35*cos(1)^35) + sin(1)^39/(39*cos(1)^39) + sin(1)^43/(43*cos(1)^43) + sin(1)^47/(47*cos(1)^47) + sin(1)^51/(51*cos(1)^51)

Respuesta numérica [src]

89114032.418624

89114032.418624

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Integral de tg^52x dx

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