Sr Examen
Integral de (1/(2sinx+cosx+2)) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------------------- dx | 2*sin(x) + cos(x) + 2 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(2 \sin{\left(x \right)} + \cos{\left(x \right)}\right) + 2}\, dx$$
Integral(1/(2*sin(x) + cos(x) + 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 1 / /x\\ / /x\\ | --------------------- dx = C - log|3 + tan|-|| + log|1 + tan|-|| | 2*sin(x) + cos(x) + 2 \ \2// \ \2// | /
$$\int \frac{1}{\left(2 \sin{\left(x \right)} + \cos{\left(x \right)}\right) + 2}\, dx = C + \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} + 3 \right)}$$
Gráfica
Respuesta
[src]
-log(3 + tan(1/2)) + log(3) + log(1 + tan(1/2))
$$- \log{\left(\tan{\left(\frac{1}{2} \right)} + 3 \right)} + \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} + \log{\left(3 \right)}$$
=
=
-log(3 + tan(1/2)) + log(3) + log(1 + tan(1/2))
$$- \log{\left(\tan{\left(\frac{1}{2} \right)} + 3 \right)} + \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} + \log{\left(3 \right)}$$
-log(3 + tan(1/2)) + log(3) + log(1 + tan(1/2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.