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Resolución de integrales/ sinx\x^2

Integral de sinx\x^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo          
  /          
 |           
 |  sin(x)   
 |  ------ dx
 |     2     
 |    x      
 |           
/            
1
∫1∞sin⁡(x)x2 dx\int\limits_{1}^{\infty} \frac{\sin{\left(x \right)}}{x^{2}}\, dx 
Integral(sin(x)/x^2, (x, 1, oo))
Respuesta (Indefinida) [src] 
  /                  /         
 |                  |          
 | sin(x)           | sin(x)   
 | ------ dx = C +  | ------ dx
 |    2             |    2     
 |   x              |   x      
 |                  |          
/                  /
∫sin⁡(x)x2 dx=C+∫sin⁡(x)x2 dx\int \frac{\sin{\left(x \right)}}{x^{2}}\, dx = C + \int \frac{\sin{\left(x \right)}}{x^{2}}\, dx
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
π(−2log⁡(2)π−2γπ+−2−2Ci⁡(1)+2γ+2sin⁡(1)π+log⁡(4)π+2π)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
π(−2log⁡(2)π−2γπ+−2−2Ci⁡(1)+2γ+2sin⁡(1)π+log⁡(4)π+2π)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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