Sr Examen
Integral de (sqrt(3)/(2+cosx))cosx dx
Solución
Ha introducido
[src]
1 / | | ___ | \/ 3 | ----------*cos(x) dx | 2 + cos(x) | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{3}}{\cos{\left(x \right)} + 2} \cos{\left(x \right)}\, dx$$
Integral((sqrt(3)/(2 + cos(x)))*cos(x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / /x pi\ / ___ /x\\\\ / | | |- - --| |\/ 3 *tan|-|||| | | ___ | |2 2 | | \2/||| | ___ | 4*\/ 3 *|pi*floor|------| + atan|------------||| | \/ 3 ___ | \ \ pi / \ 3 //| | ----------*cos(x) dx = C + \/ 3 *|x - -----------------------------------------------| | 2 + cos(x) \ 3 / | /
$$\int \frac{\sqrt{3}}{\cos{\left(x \right)} + 2} \cos{\left(x \right)}\, dx = C + \sqrt{3} \left(x - \frac{4 \sqrt{3} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}\right)$$
Gráfica
Respuesta
[src]
/ / / ___ \\\
| ___ | |\/ 3 *tan(1/2)|||
| 4*\/ 3 *|-pi + atan|--------------|||
___ | \ \ 3 //|
-4*pi + \/ 3 *|1 - ------------------------------------|
\ 3 /
$$- 4 \pi + \sqrt{3} \left(1 - \frac{4 \sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{3}\right)$$
=
=
/ / / ___ \\\
| ___ | |\/ 3 *tan(1/2)|||
| 4*\/ 3 *|-pi + atan|--------------|||
___ | \ \ 3 //|
-4*pi + \/ 3 *|1 - ------------------------------------|
\ 3 /
$$- 4 \pi + \sqrt{3} \left(1 - \frac{4 \sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{3}\right)$$
-4*pi + sqrt(3)*(1 - 4*sqrt(3)*(-pi + atan(sqrt(3)*tan(1/2)/3))/3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.