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