Sr Examen
Integral de 1/(3+cos4x) dx
Solución
Ha introducido
[src]
pi -- 3 / | | 1 | ------------ dx | 3 + cos(4*x) | / pi -- 6
$$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{\cos{\left(4 x \right)} + 3}\, dx$$
Integral(1/(3 + cos(4*x)), (x, pi/6, pi/3))
Respuesta (Indefinida)
[src]
/ / pi\ \
| |2*x - --| / ___ \|
/ ___ | | 2 | |\/ 2 *tan(2*x)||
| \/ 2 *|pi*floor|--------| + atan|--------------||
| 1 \ \ pi / \ 2 //
| ------------ dx = C + -------------------------------------------------
| 3 + cos(4*x) 8
|
/
$$\int \frac{1}{\cos{\left(4 x \right)} + 3}\, dx = C + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(2 x \right)}}{2} \right)} + \pi \left\lfloor{\frac{2 x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{8}$$
Gráfica
Respuesta
[src]
/ / ___\\ / ___\
___ | |\/ 6 || ___ |\/ 6 |
\/ 2 *|-pi + atan|-----|| \/ 2 *atan|-----|
\ \ 2 // \ 2 /
- ------------------------- - -----------------
8 8
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{6}}{2} \right)}}{8} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{2} \right)}\right)}{8}$$
=
=
/ / ___\\ / ___\
___ | |\/ 6 || ___ |\/ 6 |
\/ 2 *|-pi + atan|-----|| \/ 2 *atan|-----|
\ \ 2 // \ 2 /
- ------------------------- - -----------------
8 8
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{6}}{2} \right)}}{8} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{2} \right)}\right)}{8}$$
-sqrt(2)*(-pi + atan(sqrt(6)/2))/8 - sqrt(2)*atan(sqrt(6)/2)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.