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Resolución de integrales/ sin^2/ (2x+5)/ sin^2(2x+5)

Integral de sin^2(2x+5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |     2            
 |  sin (2*x + 5) dx
 |                  
/                   
0
$$\int\limits_{0}^{1} \sin^{2}{\left(2 x + 5 \right)}\, dx$$ 
Integral(sin(2*x + 5)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                            
 |                                                                               3                                                                                4                                        2                   
 |    2                                     x                                 tan (5/2 + x)                            tan(5/2 + x)                          x*tan (5/2 + x)                        2*x*tan (5/2 + x)          
 | sin (2*x + 5) dx = C + ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + -------------------------------------
 |                                 4                 2                     4                 2                     4                 2                     4                 2                     4                 2         
/                         2 + 2*tan (5/2 + x) + 4*tan (5/2 + x)   2 + 2*tan (5/2 + x) + 4*tan (5/2 + x)   2 + 2*tan (5/2 + x) + 4*tan (5/2 + x)   2 + 2*tan (5/2 + x) + 4*tan (5/2 + x)   2 + 2*tan (5/2 + x) + 4*tan (5/2 + x)
$$\int \sin^{2}{\left(2 x + 5 \right)}\, dx = C + \frac{x \tan^{4}{\left(x + \frac{5}{2} \right)}}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2} + \frac{2 x \tan^{2}{\left(x + \frac{5}{2} \right)}}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2} + \frac{x}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2} + \frac{\tan^{3}{\left(x + \frac{5}{2} \right)}}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2} - \frac{\tan{\left(x + \frac{5}{2} \right)}}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2         2                                   
cos (7)   sin (7)   cos(7)*sin(7)   cos(5)*sin(5)
------- + ------- - ------------- + -------------
   2         2            4               4
$$- \frac{\sin{\left(7 \right)} \cos{\left(7 \right)}}{4} + \frac{\sin{\left(5 \right)} \cos{\left(5 \right)}}{4} + \frac{\sin^{2}{\left(7 \right)}}{2} + \frac{\cos^{2}{\left(7 \right)}}{2}$$ 
=
= 
   2         2                                   
cos (7)   sin (7)   cos(7)*sin(7)   cos(5)*sin(5)
------- + ------- - ------------- + -------------
   2         2            4               4
$$- \frac{\sin{\left(7 \right)} \cos{\left(7 \right)}}{4} + \frac{\sin{\left(5 \right)} \cos{\left(5 \right)}}{4} + \frac{\sin^{2}{\left(7 \right)}}{2} + \frac{\cos^{2}{\left(7 \right)}}{2}$$ 
cos(7)^2/2 + sin(7)^2/2 - cos(7)*sin(7)/4 + cos(5)*sin(5)/4
Respuesta numérica [src] 
0.30817144167697
0.30817144167697

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

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