Sr Examen
Integral de (2-3sinx)/((1-2sinx)*cosx) dx
Solución
Ha introducido
[src]
-2*pi
/
|
| 2 - 3*sin(x)
| --------------------- dx
| (1 - 2*sin(x))*cos(x)
|
/
-13*pi
------
6
$$\int\limits_{- \frac{13 \pi}{6}}^{- 2 \pi} \frac{2 - 3 \sin{\left(x \right)}}{\left(1 - 2 \sin{\left(x \right)}\right) \cos{\left(x \right)}}\, dx$$
Integral((2 - 3*sin(x))/(((1 - 2*sin(x))*cos(x))), (x, -13*pi/6, -2*pi))
Respuesta (Indefinida)
[src]
/ / 2/x\ /x\\ / /x\\ | log|1 + tan |-| - 4*tan|-|| 5*log|1 + tan|-|| | 2 - 3*sin(x) / /x\\ \ \2/ \2// \ \2// | --------------------- dx = C - log|-1 + tan|-|| - --------------------------- + ----------------- | (1 - 2*sin(x))*cos(x) \ \2// 3 3 | /
$$\int \frac{2 - 3 \sin{\left(x \right)}}{\left(1 - 2 \sin{\left(x \right)}\right) \cos{\left(x \right)}}\, dx = C - \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + \frac{5 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{3} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 4 \tan{\left(\frac{x}{2} \right)} + 1 \right)}}{3}$$
Gráfica
Respuesta
[src]
/ 2 \
/ ___\ | / ___\ ___|
5*log\-1 + \/ 3 / log\9 + \-2 + \/ 3 / - 4*\/ 3 / / ___\
- ----------------- + -------------------------------- + log\3 - \/ 3 /
3 3
$$\log{\left(3 - \sqrt{3} \right)} + \frac{\log{\left(- 4 \sqrt{3} + \left(-2 + \sqrt{3}\right)^{2} + 9 \right)}}{3} - \frac{5 \log{\left(-1 + \sqrt{3} \right)}}{3}$$
=
=
/ 2 \
/ ___\ | / ___\ ___|
5*log\-1 + \/ 3 / log\9 + \-2 + \/ 3 / - 4*\/ 3 / / ___\
- ----------------- + -------------------------------- + log\3 - \/ 3 /
3 3
$$\log{\left(3 - \sqrt{3} \right)} + \frac{\log{\left(- 4 \sqrt{3} + \left(-2 + \sqrt{3}\right)^{2} + 9 \right)}}{3} - \frac{5 \log{\left(-1 + \sqrt{3} \right)}}{3}$$
-5*log(-1 + sqrt(3))/3 + log(9 + (-2 + sqrt(3))^2 - 4*sqrt(3))/3 + log(3 - sqrt(3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.