Sr Examen
Integral de cos2x/x dx
Solución
Ha introducido
[src]
oo / | | cos(2*x) | -------- dx | x | / 1
$$\int\limits_{1}^{\infty} \frac{\cos{\left(2 x \right)}}{x}\, dx$$
Integral(cos(2*x)/x, (x, 1, oo))
Solución detallada
-
Añadimos la constante de integración:
CiRule(a=2, b=0, context=cos(2*x)/x, symbol=x)
Respuesta:
Respuesta (Indefinida)
[src]
/ | | cos(2*x) | -------- dx = C + Ci(2*x) | x | /
$$\int \frac{\cos{\left(2 x \right)}}{x}\, dx = C + \operatorname{Ci}{\left(2 x \right)}$$
Gráfica
Respuesta
[src]
| / / pi*I\\ |
| | | ----|| |
| | pi*I | 2 || |
| 2*|-Ci(2) - ---- + EulerGamma + log\2*e /| |
____ | \ 2 / 2*EulerGamma 2*log(2)|
-\/ pi *|- --------------------------------------------- + ------------ + --------|
| ____ ____ ____ |
| \/ pi \/ pi \/ pi |
------------------------------------------------------------------------------------
2
$$- \frac{\sqrt{\pi} \left|{\frac{2 \gamma}{\sqrt{\pi}} + \frac{2 \log{\left(2 \right)}}{\sqrt{\pi}} - \frac{2 \left(- \operatorname{Ci}{\left(2 \right)} + \gamma - \frac{i \pi}{2} + \log{\left(2 e^{\frac{i \pi}{2}} \right)}\right)}{\sqrt{\pi}}}\right|}{2}$$
=
=
| / / pi*I\\ |
| | | ----|| |
| | pi*I | 2 || |
| 2*|-Ci(2) - ---- + EulerGamma + log\2*e /| |
____ | \ 2 / 2*EulerGamma 2*log(2)|
-\/ pi *|- --------------------------------------------- + ------------ + --------|
| ____ ____ ____ |
| \/ pi \/ pi \/ pi |
------------------------------------------------------------------------------------
2
$$- \frac{\sqrt{\pi} \left|{\frac{2 \gamma}{\sqrt{\pi}} + \frac{2 \log{\left(2 \right)}}{\sqrt{\pi}} - \frac{2 \left(- \operatorname{Ci}{\left(2 \right)} + \gamma - \frac{i \pi}{2} + \log{\left(2 e^{\frac{i \pi}{2}} \right)}\right)}{\sqrt{\pi}}}\right|}{2}$$
-sqrt(pi)*Abs(-2*(-Ci(2) - pi*i/2 + EulerGamma + log(2*exp_polar(pi*i/2)))/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.