Sr Examen
Integral de 1/(3cos(x)-2sin(x)+9) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------------------- dx | 3*cos(x) - 2*sin(x) + 9 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(- 2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right) + 9}\, dx$$
Integral(1/(3*cos(x) - 2*sin(x) + 9), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ____ /x\\\
| |- - --| | ____ 3*\/ 17 *tan|-|||
/ ____ | |2 2 | | \/ 17 \2/||
| \/ 17 *|pi*floor|------| + atan|- ------ + ---------------||
| 1 \ \ pi / \ 17 17 //
| ----------------------- dx = C + ------------------------------------------------------------
| 3*cos(x) - 2*sin(x) + 9 17
|
/
$$\int \frac{1}{\left(- 2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right) + 9}\, dx = C + \frac{\sqrt{17} \left(\operatorname{atan}{\left(\frac{3 \sqrt{17} \tan{\left(\frac{x}{2} \right)}}{17} - \frac{\sqrt{17}}{17} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{17}$$
Gráfica
Respuesta
[src]
/ / ____\\ / / ____ ____ \\
____ | |\/ 17 || ____ | |\/ 17 3*\/ 17 *tan(1/2)||
\/ 17 *|-pi - atan|------|| \/ 17 *|-pi - atan|------ - -----------------||
\ \ 17 // \ \ 17 17 //
- --------------------------- + -----------------------------------------------
17 17
$$\frac{\sqrt{17} \left(- \pi - \operatorname{atan}{\left(- \frac{3 \sqrt{17} \tan{\left(\frac{1}{2} \right)}}{17} + \frac{\sqrt{17}}{17} \right)}\right)}{17} - \frac{\sqrt{17} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{17}}{17} \right)}\right)}{17}$$
=
=
/ / ____\\ / / ____ ____ \\
____ | |\/ 17 || ____ | |\/ 17 3*\/ 17 *tan(1/2)||
\/ 17 *|-pi - atan|------|| \/ 17 *|-pi - atan|------ - -----------------||
\ \ 17 // \ \ 17 17 //
- --------------------------- + -----------------------------------------------
17 17
$$\frac{\sqrt{17} \left(- \pi - \operatorname{atan}{\left(- \frac{3 \sqrt{17} \tan{\left(\frac{1}{2} \right)}}{17} + \frac{\sqrt{17}}{17} \right)}\right)}{17} - \frac{\sqrt{17} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{17}}{17} \right)}\right)}{17}$$
-sqrt(17)*(-pi - atan(sqrt(17)/17))/17 + sqrt(17)*(-pi - atan(sqrt(17)/17 - 3*sqrt(17)*tan(1/2)/17))/17
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.