Sr Examen
Integral de (1+ctgx)/(sinx+2cosx)² dx
Solución
Ha introducido
[src]
atan(3)
/
|
| 1 + cot(x)
| -------------------- dx
| 2
| (sin(x) + 2*cos(x))
|
/
pi
--
5
$$\int\limits_{\frac{\pi}{5}}^{\operatorname{atan}{\left(3 \right)}} \frac{\cot{\left(x \right)} + 1}{\left(\sin{\left(x \right)} + 2 \cos{\left(x \right)}\right)^{2}}\, dx$$
Integral((1 + cot(x))/(sin(x) + 2*cos(x))^2, (x, pi/5, atan(3)))
Respuesta (Indefinida)
[src]
/ /x\ / | tan|-| | | 1 + cot(x) \2/ | cot(x) | -------------------- dx = C - ------------------------- + | -------------------- dx | 2 /x\ 2/x\ | 2 | (sin(x) + 2*cos(x)) -2 - 2*tan|-| + 2*tan |-| | (2*cos(x) + sin(x)) | \2/ \2/ | / /
$$\int \frac{\cot{\left(x \right)} + 1}{\left(\sin{\left(x \right)} + 2 \cos{\left(x \right)}\right)^{2}}\, dx = C + \int \frac{\cot{\left(x \right)}}{\left(\sin{\left(x \right)} + 2 \cos{\left(x \right)}\right)^{2}}\, dx - \frac{\tan{\left(\frac{x}{2} \right)}}{2 \tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 2}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.