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Resolución de integrales/ (x)^4/ sinx/(x)^4

Integral de sinx/(x)^4 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo          
  /          
 |           
 |  sin(x)   
 |  ------ dx
 |     4     
 |    x      
 |           
/            
1
$$\int\limits_{1}^{\infty} \frac{\sin{\left(x \right)}}{x^{4}}\, dx$$ 
Integral(sin(x)/x^4, (x, 1, oo))
Respuesta (Indefinida) [src] 
  /                  /         
 |                  |          
 | sin(x)           | sin(x)   
 | ------ dx = C +  | ------ dx
 |    4             |    4     
 |   x              |   x      
 |                  |          
/                  /
$$\int \frac{\sin{\left(x \right)}}{x^{4}}\, dx = C + \int \frac{\sin{\left(x \right)}}{x^{4}}\, dx$$
Simplificar
Respuesta [src] 
       /              7    EulerGamma   Ci(1)   cos(1)   sin(1)                                   \
       |            - -- - ---------- + ----- + ------ + ------                                   |
  ____ |    7         18       3          3       3        3       log(4)    EulerGamma    log(2) |
\/ pi *|--------- + ------------------------------------------- - -------- + ---------- + --------|
       |     ____                        ____                         ____        ____        ____|
       \18*\/ pi                       \/ pi                      6*\/ pi     3*\/ pi     3*\/ pi /
---------------------------------------------------------------------------------------------------
                                                 2
$$\frac{\sqrt{\pi} \left(- \frac{\log{\left(4 \right)}}{6 \sqrt{\pi}} + \frac{- \frac{7}{18} - \frac{\gamma}{3} + \frac{\operatorname{Ci}{\left(1 \right)}}{3} + \frac{\cos{\left(1 \right)}}{3} + \frac{\sin{\left(1 \right)}}{3}}{\sqrt{\pi}} + \frac{\gamma}{3 \sqrt{\pi}} + \frac{\log{\left(2 \right)}}{3 \sqrt{\pi}} + \frac{7}{18 \sqrt{\pi}}\right)}{2}$$ 
=
= 
       /              7    EulerGamma   Ci(1)   cos(1)   sin(1)                                   \
       |            - -- - ---------- + ----- + ------ + ------                                   |
  ____ |    7         18       3          3       3        3       log(4)    EulerGamma    log(2) |
\/ pi *|--------- + ------------------------------------------- - -------- + ---------- + --------|
       |     ____                        ____                         ____        ____        ____|
       \18*\/ pi                       \/ pi                      6*\/ pi     3*\/ pi     3*\/ pi /
---------------------------------------------------------------------------------------------------
                                                 2
$$\frac{\sqrt{\pi} \left(- \frac{\log{\left(4 \right)}}{6 \sqrt{\pi}} + \frac{- \frac{7}{18} - \frac{\gamma}{3} + \frac{\operatorname{Ci}{\left(1 \right)}}{3} + \frac{\cos{\left(1 \right)}}{3} + \frac{\sin{\left(1 \right)}}{3}}{\sqrt{\pi}} + \frac{\gamma}{3 \sqrt{\pi}} + \frac{\log{\left(2 \right)}}{3 \sqrt{\pi}} + \frac{7}{18 \sqrt{\pi}}\right)}{2}$$ 
sqrt(pi)*(7/(18*sqrt(pi)) + (-7/18 - EulerGamma/3 + Ci(1)/3 + cos(1)/3 + sin(1)/3)/sqrt(pi) - log(4)/(6*sqrt(pi)) + EulerGamma/(3*sqrt(pi)) + log(2)/(3*sqrt(pi)))/2

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

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