Sr Examen
Integral de 1/(2sin(x)+5) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 2*sin(x) + 5 | / 0
$$\int\limits_{0}^{1} \frac{1}{2 \sin{\left(x \right)} + 5}\, dx$$
Integral(1/(2*sin(x) + 5), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ____ /x\\\
| |- - --| | ____ 5*\/ 21 *tan|-|||
/ ____ | |2 2 | |2*\/ 21 \2/||
| 2*\/ 21 *|pi*floor|------| + atan|-------- + ---------------||
| 1 \ \ pi / \ 21 21 //
| ------------ dx = C + --------------------------------------------------------------
| 2*sin(x) + 5 21
|
/
$$\int \frac{1}{2 \sin{\left(x \right)} + 5}\, dx = C + \frac{2 \sqrt{21} \left(\operatorname{atan}{\left(\frac{5 \sqrt{21} \tan{\left(\frac{x}{2} \right)}}{21} + \frac{2 \sqrt{21}}{21} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{21}$$
Gráfica
Respuesta
[src]
/ / ____\\ / / ____ ____ \\
____ | |2*\/ 21 || ____ | |2*\/ 21 5*\/ 21 *tan(1/2)||
2*\/ 21 *|-pi + atan|--------|| 2*\/ 21 *|-pi + atan|-------- + -----------------||
\ \ 21 // \ \ 21 21 //
- ------------------------------- + ---------------------------------------------------
21 21
$$\frac{2 \sqrt{21} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} + \frac{5 \sqrt{21} \tan{\left(\frac{1}{2} \right)}}{21} \right)}\right)}{21} - \frac{2 \sqrt{21} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)}\right)}{21}$$
=
=
/ / ____\\ / / ____ ____ \\
____ | |2*\/ 21 || ____ | |2*\/ 21 5*\/ 21 *tan(1/2)||
2*\/ 21 *|-pi + atan|--------|| 2*\/ 21 *|-pi + atan|-------- + -----------------||
\ \ 21 // \ \ 21 21 //
- ------------------------------- + ---------------------------------------------------
21 21
$$\frac{2 \sqrt{21} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} + \frac{5 \sqrt{21} \tan{\left(\frac{1}{2} \right)}}{21} \right)}\right)}{21} - \frac{2 \sqrt{21} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)}\right)}{21}$$
-2*sqrt(21)*(-pi + atan(2*sqrt(21)/21))/21 + 2*sqrt(21)*(-pi + atan(2*sqrt(21)/21 + 5*sqrt(21)*tan(1/2)/21))/21
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.