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Resolución de integrales/ cos^2/ (5x+3)/ cos^2(5x+3)

Integral de cos^2(5x+3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
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 |     2            
 |  cos (5*x + 3) dx
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0
$$\int\limits_{0}^{1} \cos^{2}{\left(5 x + 3 \right)}\, dx$$ 
Integral(cos(5*x + 3)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                        3/3   5*x\                                  /3   5*x\                                                                             4/3   5*x\                                  2/3   5*x\           
 |                                    2*tan |- + ---|                             2*tan|- + ---|                                                                      5*x*tan |- + ---|                          10*x*tan |- + ---|           
 |    2                                     \2    2 /                                  \2    2 /                                  5*x                                         \2    2 /                                   \2    2 /           
 | cos (5*x + 3) dx = C - ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ----------------------------------------
 |                                   4/3   5*x\         2/3   5*x\              4/3   5*x\         2/3   5*x\              4/3   5*x\         2/3   5*x\              4/3   5*x\         2/3   5*x\              4/3   5*x\         2/3   5*x\
/                         10 + 10*tan |- + ---| + 20*tan |- + ---|   10 + 10*tan |- + ---| + 20*tan |- + ---|   10 + 10*tan |- + ---| + 20*tan |- + ---|   10 + 10*tan |- + ---| + 20*tan |- + ---|   10 + 10*tan |- + ---| + 20*tan |- + ---|
                                      \2    2 /          \2    2 /               \2    2 /          \2    2 /               \2    2 /          \2    2 /               \2    2 /          \2    2 /               \2    2 /          \2    2 /
$$\int \cos^{2}{\left(5 x + 3 \right)}\, dx = C + \frac{5 x \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10} + \frac{10 x \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10} + \frac{5 x}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10} - \frac{2 \tan^{3}{\left(\frac{5 x}{2} + \frac{3}{2} \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10} + \frac{2 \tan{\left(\frac{5 x}{2} + \frac{3}{2} \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2         2                                   
cos (8)   sin (8)   cos(3)*sin(3)   cos(8)*sin(8)
------- + ------- - ------------- + -------------
   2         2            10              10
$$\frac{\sin{\left(8 \right)} \cos{\left(8 \right)}}{10} + \frac{\cos^{2}{\left(8 \right)}}{2} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{10} + \frac{\sin^{2}{\left(8 \right)}}{2}$$ 
=
= 
   2         2                                   
cos (8)   sin (8)   cos(3)*sin(3)   cos(8)*sin(8)
------- + ------- - ------------- + -------------
   2         2            10              10
$$\frac{\sin{\left(8 \right)} \cos{\left(8 \right)}}{10} + \frac{\cos^{2}{\left(8 \right)}}{2} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{10} + \frac{\sin^{2}{\left(8 \right)}}{2}$$ 
cos(8)^2/2 + sin(8)^2/2 - cos(3)*sin(3)/10 + cos(8)*sin(8)/10
Respuesta numérica [src] 
0.499575609076693
0.499575609076693

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

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