Sr Examen
Integral de 1/(4+3sinx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 4 + 3*sin(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{3 \sin{\left(x \right)} + 4}\, dx$$
Integral(1/(4 + 3*sin(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| | ___ 4*\/ 7 *tan|-|||
/ ___ | |2 2 | |3*\/ 7 \2/||
| 2*\/ 7 *|pi*floor|------| + atan|------- + --------------||
| 1 \ \ pi / \ 7 7 //
| ------------ dx = C + -----------------------------------------------------------
| 4 + 3*sin(x) 7
|
/
$$\int \frac{1}{3 \sin{\left(x \right)} + 4}\, dx = C + \frac{2 \sqrt{7} \left(\operatorname{atan}{\left(\frac{4 \sqrt{7} \tan{\left(\frac{x}{2} \right)}}{7} + \frac{3 \sqrt{7}}{7} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{7}$$
Gráfica
Respuesta
[src]
/ / ___\\ / / ___ ___ \\
___ | |3*\/ 7 || ___ | |3*\/ 7 4*\/ 7 *tan(1/2)||
2*\/ 7 *|-pi + atan|-------|| 2*\/ 7 *|-pi + atan|------- + ----------------||
\ \ 7 // \ \ 7 7 //
- ----------------------------- + ------------------------------------------------
7 7
$$\frac{2 \sqrt{7} \left(- \pi + \operatorname{atan}{\left(\frac{4 \sqrt{7} \tan{\left(\frac{1}{2} \right)}}{7} + \frac{3 \sqrt{7}}{7} \right)}\right)}{7} - \frac{2 \sqrt{7} \left(- \pi + \operatorname{atan}{\left(\frac{3 \sqrt{7}}{7} \right)}\right)}{7}$$
=
=
/ / ___\\ / / ___ ___ \\
___ | |3*\/ 7 || ___ | |3*\/ 7 4*\/ 7 *tan(1/2)||
2*\/ 7 *|-pi + atan|-------|| 2*\/ 7 *|-pi + atan|------- + ----------------||
\ \ 7 // \ \ 7 7 //
- ----------------------------- + ------------------------------------------------
7 7
$$\frac{2 \sqrt{7} \left(- \pi + \operatorname{atan}{\left(\frac{4 \sqrt{7} \tan{\left(\frac{1}{2} \right)}}{7} + \frac{3 \sqrt{7}}{7} \right)}\right)}{7} - \frac{2 \sqrt{7} \left(- \pi + \operatorname{atan}{\left(\frac{3 \sqrt{7}}{7} \right)}\right)}{7}$$
-2*sqrt(7)*(-pi + atan(3*sqrt(7)/7))/7 + 2*sqrt(7)*(-pi + atan(3*sqrt(7)/7 + 4*sqrt(7)*tan(1/2)/7))/7
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.