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Resolución de integrales/ (2x+5)/ sin^2/ 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                 
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 |  sin (2*x + 5) dx
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0
∫01sin⁡2(2x+5) dx\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)
∫sin⁡2(2x+5) dx=C+xtan⁡4(x+52)2tan⁡4(x+52)+4tan⁡2(x+52)+2+2xtan⁡2(x+52)2tan⁡4(x+52)+4tan⁡2(x+52)+2+x2tan⁡4(x+52)+4tan⁡2(x+52)+2+tan⁡3(x+52)2tan⁡4(x+52)+4tan⁡2(x+52)+2−tan⁡(x+52)2tan⁡4(x+52)+4tan⁡2(x+52)+2\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
0.001.000.100.200.300.400.500.600.700.800.900.01.0
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
−sin⁡(7)cos⁡(7)4+sin⁡(5)cos⁡(5)4+sin⁡2(7)2+cos⁡2(7)2- \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
−sin⁡(7)cos⁡(7)4+sin⁡(5)cos⁡(5)4+sin⁡2(7)2+cos⁡2(7)2- \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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