Sr Examen
Integral de (1)/(3+2sin(x)) dx
Solución
Ha introducido
[src]
4*pi / | | 1 | ------------ dx | 3 + 2*sin(x) | / 0
$$\int\limits_{0}^{4 \pi} \frac{1}{2 \sin{\left(x \right)} + 3}\, dx$$
Integral(1/(3 + 2*sin(x)), (x, 0, 4*pi))
Respuesta (Indefinida)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| | ___ 3*\/ 5 *tan|-|||
/ ___ | |2 2 | |2*\/ 5 \2/||
| 2*\/ 5 *|pi*floor|------| + atan|------- + --------------||
| 1 \ \ pi / \ 5 5 //
| ------------ dx = C + -----------------------------------------------------------
| 3 + 2*sin(x) 5
|
/
$$\int \frac{1}{2 \sin{\left(x \right)} + 3}\, dx = C + \frac{2 \sqrt{5} \left(\operatorname{atan}{\left(\frac{3 \sqrt{5} \tan{\left(\frac{x}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{5}$$
Gráfica
Respuesta
[src]
/ / ___\\ / / ___\\
___ | |2*\/ 5 || ___ | |2*\/ 5 ||
2*\/ 5 *|-pi + atan|-------|| 2*\/ 5 *|pi + atan|-------||
\ \ 5 // \ \ 5 //
- ----------------------------- + ----------------------------
5 5
$$- \frac{2 \sqrt{5} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}\right)}{5} + \frac{2 \sqrt{5} \left(\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)} + \pi\right)}{5}$$
=
=
/ / ___\\ / / ___\\
___ | |2*\/ 5 || ___ | |2*\/ 5 ||
2*\/ 5 *|-pi + atan|-------|| 2*\/ 5 *|pi + atan|-------||
\ \ 5 // \ \ 5 //
- ----------------------------- + ----------------------------
5 5
$$- \frac{2 \sqrt{5} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}\right)}{5} + \frac{2 \sqrt{5} \left(\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)} + \pi\right)}{5}$$
-2*sqrt(5)*(-pi + atan(2*sqrt(5)/5))/5 + 2*sqrt(5)*(pi + atan(2*sqrt(5)/5))/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.