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Resolución de integrales/ cos^2/ cos^2(6t+5)

Integral de cos^2(6t+5) dt

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
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 |     2            
 |  cos (6*t + 5) dt
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0
$$\int\limits_{0}^{1} \cos^{2}{\left(6 t + 5 \right)}\, dt$$ 
Integral(cos(6*t + 5)^2, (t, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                     
 |                                                                                     3                                                                                           4                                            2                       
 |    2                                 tan(5/2 + 3*t)                              tan (5/2 + 3*t)                                    3*t                                  3*t*tan (5/2 + 3*t)                          6*t*tan (5/2 + 3*t)            
 | cos (6*t + 5) dt = C + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + ------------------------------------------ + ------------------------------------------
 |                                 4                    2                       4                    2                       4                    2                       4                    2                       4                    2           
/                         6 + 6*tan (5/2 + 3*t) + 12*tan (5/2 + 3*t)   6 + 6*tan (5/2 + 3*t) + 12*tan (5/2 + 3*t)   6 + 6*tan (5/2 + 3*t) + 12*tan (5/2 + 3*t)   6 + 6*tan (5/2 + 3*t) + 12*tan (5/2 + 3*t)   6 + 6*tan (5/2 + 3*t) + 12*tan (5/2 + 3*t)
$$\int \cos^{2}{\left(6 t + 5 \right)}\, dt = C + \frac{3 t \tan^{4}{\left(3 t + \frac{5}{2} \right)}}{6 \tan^{4}{\left(3 t + \frac{5}{2} \right)} + 12 \tan^{2}{\left(3 t + \frac{5}{2} \right)} + 6} + \frac{6 t \tan^{2}{\left(3 t + \frac{5}{2} \right)}}{6 \tan^{4}{\left(3 t + \frac{5}{2} \right)} + 12 \tan^{2}{\left(3 t + \frac{5}{2} \right)} + 6} + \frac{3 t}{6 \tan^{4}{\left(3 t + \frac{5}{2} \right)} + 12 \tan^{2}{\left(3 t + \frac{5}{2} \right)} + 6} - \frac{\tan^{3}{\left(3 t + \frac{5}{2} \right)}}{6 \tan^{4}{\left(3 t + \frac{5}{2} \right)} + 12 \tan^{2}{\left(3 t + \frac{5}{2} \right)} + 6} + \frac{\tan{\left(3 t + \frac{5}{2} \right)}}{6 \tan^{4}{\left(3 t + \frac{5}{2} \right)} + 12 \tan^{2}{\left(3 t + \frac{5}{2} \right)} + 6}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2          2                                      
cos (11)   sin (11)   cos(5)*sin(5)   cos(11)*sin(11)
-------- + -------- - ------------- + ---------------
   2          2             12               12
$$\frac{\sin{\left(11 \right)} \cos{\left(11 \right)}}{12} + \frac{\cos^{2}{\left(11 \right)}}{2} - \frac{\sin{\left(5 \right)} \cos{\left(5 \right)}}{12} + \frac{\sin^{2}{\left(11 \right)}}{2}$$ 
=
= 
   2          2                                      
cos (11)   sin (11)   cos(5)*sin(5)   cos(11)*sin(11)
-------- + -------- - ------------- + ---------------
   2          2             12               12
$$\frac{\sin{\left(11 \right)} \cos{\left(11 \right)}}{12} + \frac{\cos^{2}{\left(11 \right)}}{2} - \frac{\sin{\left(5 \right)} \cos{\left(5 \right)}}{12} + \frac{\sin^{2}{\left(11 \right)}}{2}$$ 
cos(11)^2/2 + sin(11)^2/2 - cos(5)*sin(5)/12 + cos(11)*sin(11)/12
Respuesta numérica [src] 
0.52229874173329
0.52229874173329

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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