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