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Resolución de integrales/ sin(t)/ sin(t)/t^2

Integral de sin(t)/t^2 dt

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 3*x         
  /          
 |           
 |  sin(t)   
 |  ------ dt
 |     2     
 |    t      
 |           
/            
x
∫x3xsin⁡(t)t2 dt\int\limits_{x}^{3 x} \frac{\sin{\left(t \right)}}{t^{2}}\, dt 
Integral(sin(t)/t^2, (t, x, 3*x))
Respuesta (Indefinida) [src] 
  /                  /         
 |                  |          
 | sin(t)           | sin(t)   
 | ------ dt = C +  | ------ dt
 |    2             |    2     
 |   t              |   t      
 |                  |          
/                  /
∫sin⁡(t)t2 dt=C+∫sin⁡(t)t2 dt\int \frac{\sin{\left(t \right)}}{t^{2}}\, dt = C + \int \frac{\sin{\left(t \right)}}{t^{2}}\, dt
Simplificar
Respuesta [src] 
   /   2\                         / 2\                                       
log\9*x /                      log\x /   sin(x)   sin(3*x)                   
--------- - Ci(x) - log(3*x) - ------- + ------ - -------- + Ci(3*x) + log(x)
    2                             2        x        3*x
log⁡(x)−log⁡(3x)−log⁡(x2)2+log⁡(9x2)2−Ci⁡(x)+Ci⁡(3x)+sin⁡(x)x−sin⁡(3x)3x\log{\left(x \right)} - \log{\left(3 x \right)} - \frac{\log{\left(x^{2} \right)}}{2} + \frac{\log{\left(9 x^{2} \right)}}{2} - \operatorname{Ci}{\left(x \right)} + \operatorname{Ci}{\left(3 x \right)} + \frac{\sin{\left(x \right)}}{x} - \frac{\sin{\left(3 x \right)}}{3 x} 
=
= 
   /   2\                         / 2\                                       
log\9*x /                      log\x /   sin(x)   sin(3*x)                   
--------- - Ci(x) - log(3*x) - ------- + ------ - -------- + Ci(3*x) + log(x)
    2                             2        x        3*x
log⁡(x)−log⁡(3x)−log⁡(x2)2+log⁡(9x2)2−Ci⁡(x)+Ci⁡(3x)+sin⁡(x)x−sin⁡(3x)3x\log{\left(x \right)} - \log{\left(3 x \right)} - \frac{\log{\left(x^{2} \right)}}{2} + \frac{\log{\left(9 x^{2} \right)}}{2} - \operatorname{Ci}{\left(x \right)} + \operatorname{Ci}{\left(3 x \right)} + \frac{\sin{\left(x \right)}}{x} - \frac{\sin{\left(3 x \right)}}{3 x} 
log(9*x^2)/2 - Ci(x) - log(3*x) - log(x^2)/2 + sin(x)/x - sin(3*x)/(3*x) + Ci(3*x) + log(x)

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

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