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