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Resolución de integrales/ dxcos2(7x+2)

Integral de dxcos2(7x+2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |     2            
 |  cos (7*x + 2) dx
 |                  
/                   
0
$$\int\limits_{0}^{1} \cos^{2}{\left(7 x + 2 \right)}\, dx$$ 
Integral(cos(7*x + 2)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                        3/    7*x\                                  /    7*x\                                                                             4/    7*x\                                  2/    7*x\           
 |                                    2*tan |1 + ---|                             2*tan|1 + ---|                                                                      7*x*tan |1 + ---|                          14*x*tan |1 + ---|           
 |    2                                     \     2 /                                  \     2 /                                  7*x                                         \     2 /                                   \     2 /           
 | cos (7*x + 2) dx = C - ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ----------------------------------------
 |                                   4/    7*x\         2/    7*x\              4/    7*x\         2/    7*x\              4/    7*x\         2/    7*x\              4/    7*x\         2/    7*x\              4/    7*x\         2/    7*x\
/                         14 + 14*tan |1 + ---| + 28*tan |1 + ---|   14 + 14*tan |1 + ---| + 28*tan |1 + ---|   14 + 14*tan |1 + ---| + 28*tan |1 + ---|   14 + 14*tan |1 + ---| + 28*tan |1 + ---|   14 + 14*tan |1 + ---| + 28*tan |1 + ---|
                                      \     2 /          \     2 /               \     2 /          \     2 /               \     2 /          \     2 /               \     2 /          \     2 /               \     2 /          \     2 /
$$\int \cos^{2}{\left(7 x + 2 \right)}\, dx = C + \frac{7 x \tan^{4}{\left(\frac{7 x}{2} + 1 \right)}}{14 \tan^{4}{\left(\frac{7 x}{2} + 1 \right)} + 28 \tan^{2}{\left(\frac{7 x}{2} + 1 \right)} + 14} + \frac{14 x \tan^{2}{\left(\frac{7 x}{2} + 1 \right)}}{14 \tan^{4}{\left(\frac{7 x}{2} + 1 \right)} + 28 \tan^{2}{\left(\frac{7 x}{2} + 1 \right)} + 14} + \frac{7 x}{14 \tan^{4}{\left(\frac{7 x}{2} + 1 \right)} + 28 \tan^{2}{\left(\frac{7 x}{2} + 1 \right)} + 14} - \frac{2 \tan^{3}{\left(\frac{7 x}{2} + 1 \right)}}{14 \tan^{4}{\left(\frac{7 x}{2} + 1 \right)} + 28 \tan^{2}{\left(\frac{7 x}{2} + 1 \right)} + 14} + \frac{2 \tan{\left(\frac{7 x}{2} + 1 \right)}}{14 \tan^{4}{\left(\frac{7 x}{2} + 1 \right)} + 28 \tan^{2}{\left(\frac{7 x}{2} + 1 \right)} + 14}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2         2                                   
cos (9)   sin (9)   cos(2)*sin(2)   cos(9)*sin(9)
------- + ------- - ------------- + -------------
   2         2            14              14
$$\frac{\sin{\left(9 \right)} \cos{\left(9 \right)}}{14} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{14} + \frac{\sin^{2}{\left(9 \right)}}{2} + \frac{\cos^{2}{\left(9 \right)}}{2}$$ 
=
= 
   2         2                                   
cos (9)   sin (9)   cos(2)*sin(2)   cos(9)*sin(9)
------- + ------- - ------------- + -------------
   2         2            14              14
$$\frac{\sin{\left(9 \right)} \cos{\left(9 \right)}}{14} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{14} + \frac{\sin^{2}{\left(9 \right)}}{2} + \frac{\cos^{2}{\left(9 \right)}}{2}$$ 
cos(9)^2/2 + sin(9)^2/2 - cos(2)*sin(2)/14 + cos(9)*sin(9)/14
Respuesta numérica [src] 
0.500207687447723
0.500207687447723

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

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