Sr Examen
Integral de 1/(7+5cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 7 + 5*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{5 \cos{\left(x \right)} + 7}\, dx$$
Integral(1/(7 + 5*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| |\/ 6 *tan|-|||
/ ___ | |2 2 | | \2/||
| \/ 6 *|pi*floor|------| + atan|------------||
| 1 \ \ pi / \ 6 //
| ------------ dx = C + ---------------------------------------------
| 7 + 5*cos(x) 6
|
/
$$\int \frac{1}{5 \cos{\left(x \right)} + 7}\, dx = C + \frac{\sqrt{6} \left(\operatorname{atan}{\left(\frac{\sqrt{6} \tan{\left(\frac{x}{2} \right)}}{6} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{6}$$
Gráfica
Respuesta
[src]
/ / ___ \\
___ | |\/ 6 *tan(1/2)||
___ \/ 6 *|-pi + atan|--------------||
pi*\/ 6 \ \ 6 //
-------- + ----------------------------------
6 6
$$\frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6} \tan{\left(\frac{1}{2} \right)}}{6} \right)}\right)}{6} + \frac{\sqrt{6} \pi}{6}$$
=
=
/ / ___ \\
___ | |\/ 6 *tan(1/2)||
___ \/ 6 *|-pi + atan|--------------||
pi*\/ 6 \ \ 6 //
-------- + ----------------------------------
6 6
$$\frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6} \tan{\left(\frac{1}{2} \right)}}{6} \right)}\right)}{6} + \frac{\sqrt{6} \pi}{6}$$
pi*sqrt(6)/6 + sqrt(6)*(-pi + atan(sqrt(6)*tan(1/2)/6))/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.