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