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