Sr Examen
Integral de 1/(3+2sin5x) dx
Solución
Ha introducido
[src]
1 / | | 1 | -------------- dx | 3 + 2*sin(5*x) | / 0
$$\int\limits_{0}^{1} \frac{1}{2 \sin{\left(5 x \right)} + 3}\, dx$$
Integral(1/(3 + 2*sin(5*x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / pi 5*x\ / ___ /5*x\\\
| |- -- + ---| | ___ 3*\/ 5 *tan|---|||
/ ___ | | 2 2 | |2*\/ 5 \ 2 /||
| 2*\/ 5 *|pi*floor|----------| + atan|------- + ----------------||
| 1 \ \ pi / \ 5 5 //
| -------------- dx = C + -----------------------------------------------------------------
| 3 + 2*sin(5*x) 25
|
/
$$\int \frac{1}{2 \sin{\left(5 x \right)} + 3}\, dx = C + \frac{2 \sqrt{5} \left(\operatorname{atan}{\left(\frac{3 \sqrt{5} \tan{\left(\frac{5 x}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)} + \pi \left\lfloor{\frac{\frac{5 x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{25}$$
Gráfica
Respuesta
[src]
/ / ___\\ / ___ ___ \
___ | |2*\/ 5 || ___ |2*\/ 5 3*\/ 5 *tan(5/2)|
2*\/ 5 *|-pi + atan|-------|| 2*\/ 5 *atan|------- + ----------------|
\ \ 5 // \ 5 5 /
- ----------------------------- + ----------------------------------------
25 25
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{3 \sqrt{5} \tan{\left(\frac{5}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)}}{25} - \frac{2 \sqrt{5} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}\right)}{25}$$
=
=
/ / ___\\ / ___ ___ \
___ | |2*\/ 5 || ___ |2*\/ 5 3*\/ 5 *tan(5/2)|
2*\/ 5 *|-pi + atan|-------|| 2*\/ 5 *atan|------- + ----------------|
\ \ 5 // \ 5 5 /
- ----------------------------- + ----------------------------------------
25 25
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{3 \sqrt{5} \tan{\left(\frac{5}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)}}{25} - \frac{2 \sqrt{5} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}\right)}{25}$$
-2*sqrt(5)*(-pi + atan(2*sqrt(5)/5))/25 + 2*sqrt(5)*atan(2*sqrt(5)/5 + 3*sqrt(5)*tan(5/2)/5)/25
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.