Sr Examen
Integral de 1/(4-2sinx+cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------------------- dx | 4 - 2*sin(x) + cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(4 - 2 \sin{\left(x \right)}\right) + \cos{\left(x \right)}}\, dx$$
Integral(1/(4 - 2*sin(x) + cos(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ____ /x\\\
| |- - --| | ____ 3*\/ 11 *tan|-|||
/ ____ | |2 2 | | 2*\/ 11 \2/||
| 2*\/ 11 *|pi*floor|------| + atan|- -------- + ---------------||
| 1 \ \ pi / \ 11 11 //
| --------------------- dx = C + ----------------------------------------------------------------
| 4 - 2*sin(x) + cos(x) 11
|
/
$$\int \frac{1}{\left(4 - 2 \sin{\left(x \right)}\right) + \cos{\left(x \right)}}\, dx = C + \frac{2 \sqrt{11} \left(\operatorname{atan}{\left(\frac{3 \sqrt{11} \tan{\left(\frac{x}{2} \right)}}{11} - \frac{2 \sqrt{11}}{11} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{11}$$
Gráfica
Respuesta
[src]
/ / ____\\ / / ____ ____ \\
____ | |2*\/ 11 || ____ | |2*\/ 11 3*\/ 11 *tan(1/2)||
2*\/ 11 *|-pi - atan|--------|| 2*\/ 11 *|-pi - atan|-------- - -----------------||
\ \ 11 // \ \ 11 11 //
- ------------------------------- + ---------------------------------------------------
11 11
$$\frac{2 \sqrt{11} \left(- \pi - \operatorname{atan}{\left(- \frac{3 \sqrt{11} \tan{\left(\frac{1}{2} \right)}}{11} + \frac{2 \sqrt{11}}{11} \right)}\right)}{11} - \frac{2 \sqrt{11} \left(- \pi - \operatorname{atan}{\left(\frac{2 \sqrt{11}}{11} \right)}\right)}{11}$$
=
=
/ / ____\\ / / ____ ____ \\
____ | |2*\/ 11 || ____ | |2*\/ 11 3*\/ 11 *tan(1/2)||
2*\/ 11 *|-pi - atan|--------|| 2*\/ 11 *|-pi - atan|-------- - -----------------||
\ \ 11 // \ \ 11 11 //
- ------------------------------- + ---------------------------------------------------
11 11
$$\frac{2 \sqrt{11} \left(- \pi - \operatorname{atan}{\left(- \frac{3 \sqrt{11} \tan{\left(\frac{1}{2} \right)}}{11} + \frac{2 \sqrt{11}}{11} \right)}\right)}{11} - \frac{2 \sqrt{11} \left(- \pi - \operatorname{atan}{\left(\frac{2 \sqrt{11}}{11} \right)}\right)}{11}$$
-2*sqrt(11)*(-pi - atan(2*sqrt(11)/11))/11 + 2*sqrt(11)*(-pi - atan(2*sqrt(11)/11 - 3*sqrt(11)*tan(1/2)/11))/11
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.