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Resolución de integrales/ (3x+2)/ cos^2/ cos^2(3x+2)

Integral de cos^2(3x+2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
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 |     2            
 |  cos (3*x + 2) dx
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/                   
0
$$\int\limits_{0}^{1} \cos^{2}{\left(3 x + 2 \right)}\, dx$$ 
Integral(cos(3*x + 2)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                       3/    3*x\                                /    3*x\                                                                         4/    3*x\                               2/    3*x\           
 |                                   2*tan |1 + ---|                           2*tan|1 + ---|                                                                  3*x*tan |1 + ---|                        6*x*tan |1 + ---|           
 |    2                                    \     2 /                                \     2 /                                3*x                                       \     2 /                                \     2 /           
 | cos (3*x + 2) dx = C - -------------------------------------- + -------------------------------------- + -------------------------------------- + -------------------------------------- + --------------------------------------
 |                                 4/    3*x\         2/    3*x\            4/    3*x\         2/    3*x\            4/    3*x\         2/    3*x\            4/    3*x\         2/    3*x\            4/    3*x\         2/    3*x\
/                         6 + 6*tan |1 + ---| + 12*tan |1 + ---|   6 + 6*tan |1 + ---| + 12*tan |1 + ---|   6 + 6*tan |1 + ---| + 12*tan |1 + ---|   6 + 6*tan |1 + ---| + 12*tan |1 + ---|   6 + 6*tan |1 + ---| + 12*tan |1 + ---|
                                    \     2 /          \     2 /             \     2 /          \     2 /             \     2 /          \     2 /             \     2 /          \     2 /             \     2 /          \     2 /
$$\int \cos^{2}{\left(3 x + 2 \right)}\, dx = C + \frac{3 x \tan^{4}{\left(\frac{3 x}{2} + 1 \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + 1 \right)} + 12 \tan^{2}{\left(\frac{3 x}{2} + 1 \right)} + 6} + \frac{6 x \tan^{2}{\left(\frac{3 x}{2} + 1 \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + 1 \right)} + 12 \tan^{2}{\left(\frac{3 x}{2} + 1 \right)} + 6} + \frac{3 x}{6 \tan^{4}{\left(\frac{3 x}{2} + 1 \right)} + 12 \tan^{2}{\left(\frac{3 x}{2} + 1 \right)} + 6} - \frac{2 \tan^{3}{\left(\frac{3 x}{2} + 1 \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + 1 \right)} + 12 \tan^{2}{\left(\frac{3 x}{2} + 1 \right)} + 6} + \frac{2 \tan{\left(\frac{3 x}{2} + 1 \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + 1 \right)} + 12 \tan^{2}{\left(\frac{3 x}{2} + 1 \right)} + 6}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2         2                                   
cos (5)   sin (5)   cos(2)*sin(2)   cos(5)*sin(5)
------- + ------- - ------------- + -------------
   2         2            6               6
$$\frac{\sin{\left(5 \right)} \cos{\left(5 \right)}}{6} + \frac{\cos^{2}{\left(5 \right)}}{2} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{6} + \frac{\sin^{2}{\left(5 \right)}}{2}$$ 
=
= 
   2         2                                   
cos (5)   sin (5)   cos(2)*sin(2)   cos(5)*sin(5)
------- + ------- - ------------- + -------------
   2         2            6               6
$$\frac{\sin{\left(5 \right)} \cos{\left(5 \right)}}{6} + \frac{\cos^{2}{\left(5 \right)}}{2} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{6} + \frac{\sin^{2}{\left(5 \right)}}{2}$$ 
cos(5)^2/2 + sin(5)^2/2 - cos(2)*sin(2)/6 + cos(5)*sin(5)/6
Respuesta numérica [src] 
0.51773178203488
0.51773178203488

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

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