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Resolución de integrales/ Sinx/(x*x)

Integral de Sinx/(x*x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

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

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

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