Sr Examen
Integral de 1/(7+2*cosx-sinx) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------------------- dx | 7 + 2*cos(x) - sin(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(2 \cos{\left(x \right)} + 7\right) - \sin{\left(x \right)}}\, dx$$
Integral(1/(7 + 2*cos(x) - sin(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ____ /x\\\
| |- - --| | ____ 5*\/ 11 *tan|-|||
/ ____ | |2 2 | | \/ 11 \2/||
| \/ 11 *|pi*floor|------| + atan|- ------ + ---------------||
| 1 \ \ pi / \ 22 22 //
| --------------------- dx = C + ------------------------------------------------------------
| 7 + 2*cos(x) - sin(x) 11
|
/
$$\int \frac{1}{\left(2 \cos{\left(x \right)} + 7\right) - \sin{\left(x \right)}}\, dx = C + \frac{\sqrt{11} \left(\operatorname{atan}{\left(\frac{5 \sqrt{11} \tan{\left(\frac{x}{2} \right)}}{22} - \frac{\sqrt{11}}{22} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{11}$$
Gráfica
Respuesta
[src]
/ / ____\\ / / ____ ____ \\
____ | |\/ 11 || ____ | |\/ 11 5*\/ 11 *tan(1/2)||
\/ 11 *|-pi - atan|------|| \/ 11 *|-pi - atan|------ - -----------------||
\ \ 22 // \ \ 22 22 //
- --------------------------- + -----------------------------------------------
11 11
$$\frac{\sqrt{11} \left(- \pi - \operatorname{atan}{\left(- \frac{5 \sqrt{11} \tan{\left(\frac{1}{2} \right)}}{22} + \frac{\sqrt{11}}{22} \right)}\right)}{11} - \frac{\sqrt{11} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{11}}{22} \right)}\right)}{11}$$
=
=
/ / ____\\ / / ____ ____ \\
____ | |\/ 11 || ____ | |\/ 11 5*\/ 11 *tan(1/2)||
\/ 11 *|-pi - atan|------|| \/ 11 *|-pi - atan|------ - -----------------||
\ \ 22 // \ \ 22 22 //
- --------------------------- + -----------------------------------------------
11 11
$$\frac{\sqrt{11} \left(- \pi - \operatorname{atan}{\left(- \frac{5 \sqrt{11} \tan{\left(\frac{1}{2} \right)}}{22} + \frac{\sqrt{11}}{22} \right)}\right)}{11} - \frac{\sqrt{11} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{11}}{22} \right)}\right)}{11}$$
-sqrt(11)*(-pi - atan(sqrt(11)/22))/11 + sqrt(11)*(-pi - atan(sqrt(11)/22 - 5*sqrt(11)*tan(1/2)/22))/11
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.