Sr Examen
Integral de 1/(5+cosx-sinx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------------- dx | 5 + cos(x) - sin(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(\cos{\left(x \right)} + 5\right) - \sin{\left(x \right)}}\, dx$$
Integral(1/(5 + cos(x) - sin(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ____ /x\\\
| |- - --| | ____ 4*\/ 23 *tan|-|||
/ ____ | |2 2 | | \/ 23 \2/||
| 2*\/ 23 *|pi*floor|------| + atan|- ------ + ---------------||
| 1 \ \ pi / \ 23 23 //
| ------------------- dx = C + --------------------------------------------------------------
| 5 + cos(x) - sin(x) 23
|
/
$$\int \frac{1}{\left(\cos{\left(x \right)} + 5\right) - \sin{\left(x \right)}}\, dx = C + \frac{2 \sqrt{23} \left(\operatorname{atan}{\left(\frac{4 \sqrt{23} \tan{\left(\frac{x}{2} \right)}}{23} - \frac{\sqrt{23}}{23} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{23}$$
Gráfica
Respuesta
[src]
/ / ____\\ / / ____ ____ \\
____ | |\/ 23 || ____ | |\/ 23 4*\/ 23 *tan(1/2)||
2*\/ 23 *|-pi - atan|------|| 2*\/ 23 *|-pi - atan|------ - -----------------||
\ \ 23 // \ \ 23 23 //
- ----------------------------- + -------------------------------------------------
23 23
$$\frac{2 \sqrt{23} \left(- \pi - \operatorname{atan}{\left(- \frac{4 \sqrt{23} \tan{\left(\frac{1}{2} \right)}}{23} + \frac{\sqrt{23}}{23} \right)}\right)}{23} - \frac{2 \sqrt{23} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{23}}{23} \right)}\right)}{23}$$
=
=
/ / ____\\ / / ____ ____ \\
____ | |\/ 23 || ____ | |\/ 23 4*\/ 23 *tan(1/2)||
2*\/ 23 *|-pi - atan|------|| 2*\/ 23 *|-pi - atan|------ - -----------------||
\ \ 23 // \ \ 23 23 //
- ----------------------------- + -------------------------------------------------
23 23
$$\frac{2 \sqrt{23} \left(- \pi - \operatorname{atan}{\left(- \frac{4 \sqrt{23} \tan{\left(\frac{1}{2} \right)}}{23} + \frac{\sqrt{23}}{23} \right)}\right)}{23} - \frac{2 \sqrt{23} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{23}}{23} \right)}\right)}{23}$$
-2*sqrt(23)*(-pi - atan(sqrt(23)/23))/23 + 2*sqrt(23)*(-pi - atan(sqrt(23)/23 - 4*sqrt(23)*tan(1/2)/23))/23
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.