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