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