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