Sr Examen
Integral de (4*tg(x)-5)/(4*(cos(x))^2-sin(2x)+1) dx
Solución
Ha introducido
[src]
/ ___\
|2*\/ 5 |
asin|-------|
\ 5 /
/
|
| 4*tan(x) - 5
| ------------------------ dx
| 2
| 4*cos (x) - sin(2*x) + 1
|
/
pi
--
4
$$\int\limits_{\frac{\pi}{4}}^{\operatorname{asin}{\left(\frac{2 \sqrt{5}}{5} \right)}} \frac{4 \tan{\left(x \right)} - 5}{\left(- \sin{\left(2 x \right)} + 4 \cos^{2}{\left(x \right)}\right) + 1}\, dx$$
Integral((4*tan(x) - 5)/(4*cos(x)^2 - sin(2*x) + 1), (x, pi/4, asin(2*sqrt(5)/5)))
Respuesta (Indefinida)
[src]
/ / / | | | | 4*tan(x) - 5 | 1 | tan(x) | ------------------------ dx = C - 5* | ------------------------ dx + 4* | ------------------------ dx | 2 | 2 | 2 | 4*cos (x) - sin(2*x) + 1 | 4*cos (x) - sin(2*x) + 1 | 1 - sin(2*x) + 4*cos (x) | | | / / /
$$\int \frac{4 \tan{\left(x \right)} - 5}{\left(- \sin{\left(2 x \right)} + 4 \cos^{2}{\left(x \right)}\right) + 1}\, dx = C + 4 \int \frac{\tan{\left(x \right)}}{- \sin{\left(2 x \right)} + 4 \cos^{2}{\left(x \right)} + 1}\, dx - 5 \int \frac{1}{\left(- \sin{\left(2 x \right)} + 4 \cos^{2}{\left(x \right)}\right) + 1}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.