Sr Examen
Integral de 1/(3+5cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 3 + 5*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{5 \cos{\left(x \right)} + 3}\, dx$$
Integral(1/(3 + 5*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / /x\\ / /x\\ | log|-2 + tan|-|| log|2 + tan|-|| | 1 \ \2// \ \2// | ------------ dx = C - ---------------- + --------------- | 3 + 5*cos(x) 4 4 | /
$$\int \frac{1}{5 \cos{\left(x \right)} + 3}\, dx = C - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 2 \right)}}{4} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 2 \right)}}{4}$$
Gráfica
Respuesta
[src]
log(2 - tan(1/2)) log(2 + tan(1/2))
- ----------------- + -----------------
4 4
$$- \frac{\log{\left(2 - \tan{\left(\frac{1}{2} \right)} \right)}}{4} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 2 \right)}}{4}$$
=
=
log(2 - tan(1/2)) log(2 + tan(1/2))
- ----------------- + -----------------
4 4
$$- \frac{\log{\left(2 - \tan{\left(\frac{1}{2} \right)} \right)}}{4} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 2 \right)}}{4}$$
-log(2 - tan(1/2))/4 + log(2 + tan(1/2))/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.