Sr Examen
Integral de (x+2)cos(2/x) dx
Solución
Ha introducido
[src]
pi / | | /2\ | (x + 2)*cos|-| dx | \x/ | / 0
$$\int\limits_{0}^{\pi} \left(x + 2\right) \cos{\left(\frac{2}{x} \right)}\, dx$$
Integral((x + 2)*cos(2/x), (x, 0, pi))
Respuesta (Indefinida)
[src]
/ 2 /2\ | x *cos|-| | /2\ /1\ /2\ /2\ \x/ /2\ /2\ /1 \ | (x + 2)*cos|-| dx = C - 2*log|-| + 2*Ci|-| + 4*Si|-| + --------- - x*sin|-| + 2*x*cos|-| + log|--| | \x/ \x/ \x/ \x/ 2 \x/ \x/ | 2| | \x / /
$$\int \left(x + 2\right) \cos{\left(\frac{2}{x} \right)}\, dx = C + \frac{x^{2} \cos{\left(\frac{2}{x} \right)}}{2} - x \sin{\left(\frac{2}{x} \right)} + 2 x \cos{\left(\frac{2}{x} \right)} + \log{\left(\frac{1}{x^{2}} \right)} - 2 \log{\left(\frac{1}{x} \right)} + 2 \operatorname{Ci}{\left(\frac{2}{x} \right)} + 4 \operatorname{Si}{\left(\frac{2}{x} \right)}$$
Gráfica
Respuesta
[src]
2 /2 \
pi *cos|--|
/2 \ /2 \ \pi/ /2 \ /2 \
-2*pi + 2*Ci|--| + 4*Si|--| + ----------- - pi*sin|--| + 2*pi*cos|--|
\pi/ \pi/ 2 \pi/ \pi/
$$- 2 \pi - \pi \sin{\left(\frac{2}{\pi} \right)} + 2 \operatorname{Ci}{\left(\frac{2}{\pi} \right)} + 4 \operatorname{Si}{\left(\frac{2}{\pi} \right)} + \frac{\pi^{2} \cos{\left(\frac{2}{\pi} \right)}}{2} + 2 \pi \cos{\left(\frac{2}{\pi} \right)}$$
=
=
2 /2 \
pi *cos|--|
/2 \ /2 \ \pi/ /2 \ /2 \
-2*pi + 2*Ci|--| + 4*Si|--| + ----------- - pi*sin|--| + 2*pi*cos|--|
\pi/ \pi/ 2 \pi/ \pi/
$$- 2 \pi - \pi \sin{\left(\frac{2}{\pi} \right)} + 2 \operatorname{Ci}{\left(\frac{2}{\pi} \right)} + 4 \operatorname{Si}{\left(\frac{2}{\pi} \right)} + \frac{\pi^{2} \cos{\left(\frac{2}{\pi} \right)}}{2} + 2 \pi \cos{\left(\frac{2}{\pi} \right)}$$
-2*pi + 2*Ci(2/pi) + 4*Si(2/pi) + pi^2*cos(2/pi)/2 - pi*sin(2/pi) + 2*pi*cos(2/pi)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.