Sr Examen
Integral de 1/(4+2cox-sinx) dx
Solución
Ha introducido
[src]
2*pi / | | 1 | --------------------- dx | 4 + 2*cos(x) - sin(x) | / 0
$$\int\limits_{0}^{2 \pi} \frac{1}{\left(2 \cos{\left(x \right)} + 4\right) - \sin{\left(x \right)}}\, dx$$
Integral(1/(4 + 2*cos(x) - sin(x)), (x, 0, 2*pi))
Respuesta (Indefinida)
[src]
/ /x pi\ / ____ /x\\\
| |- - --| | ____ 2*\/ 11 *tan|-|||
/ ____ | |2 2 | | \/ 11 \2/||
| 2*\/ 11 *|pi*floor|------| + atan|- ------ + ---------------||
| 1 \ \ pi / \ 11 11 //
| --------------------- dx = C + --------------------------------------------------------------
| 4 + 2*cos(x) - sin(x) 11
|
/
$$\int \frac{1}{\left(2 \cos{\left(x \right)} + 4\right) - \sin{\left(x \right)}}\, dx = C + \frac{2 \sqrt{11} \left(\operatorname{atan}{\left(\frac{2 \sqrt{11} \tan{\left(\frac{x}{2} \right)}}{11} - \frac{\sqrt{11}}{11} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{11}$$
Gráfica
Respuesta
[src]
/ / ____\\ / ____\
____ | |\/ 11 || ____ |\/ 11 |
2*\/ 11 *|-pi - atan|------|| 2*\/ 11 *atan|------|
\ \ 11 // \ 11 /
- ----------------------------- - ---------------------
11 11
$$- \frac{2 \sqrt{11} \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{11} - \frac{2 \sqrt{11} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}\right)}{11}$$
=
=
/ / ____\\ / ____\
____ | |\/ 11 || ____ |\/ 11 |
2*\/ 11 *|-pi - atan|------|| 2*\/ 11 *atan|------|
\ \ 11 // \ 11 /
- ----------------------------- - ---------------------
11 11
$$- \frac{2 \sqrt{11} \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{11} - \frac{2 \sqrt{11} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}\right)}{11}$$
-2*sqrt(11)*(-pi - atan(sqrt(11)/11))/11 - 2*sqrt(11)*atan(sqrt(11)/11)/11
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.