Sr Examen
Integral de Sinx/(x*x) dx
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 | /
$$\int \frac{\sin{\left(x \right)}}{x x}\, dx = C - \log{\left(x \right)} + \frac{\log{\left(x^{2} \right)}}{2} + \operatorname{Ci}{\left(x \right)} - \frac{\sin{\left(x \right)}}{x}$$
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.