Sr Examen
Integral de 1/(5cosx^2-1) dx
Solución
Ha introducido
[src]
p - 4 / | | 1 | ------------- dx | 2 | 5*cos (x) - 1 | / 0
$$\int\limits_{0}^{\frac{p}{4}} \frac{1}{5 \cos^{2}{\left(x \right)} - 1}\, dx$$
Integral(1/(5*cos(x)^2 - 1), (x, 0, p/4))
Respuesta (Indefinida)
[src]
/ / 2/x\ /x\\ / 2/x\ /x\\ | log|-1 + tan |-| + tan|-|| log|-1 + tan |-| - tan|-|| | 1 \ \2/ \2// \ \2/ \2// | ------------- dx = C - -------------------------- + -------------------------- | 2 4 4 | 5*cos (x) - 1 | /
$$\int \frac{1}{5 \cos^{2}{\left(x \right)} - 1}\, dx = C + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{4} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{4}$$
Respuesta
[src]
/ 2/p\ /p\\ / 2/p\ /p\\
log|-1 + tan |-| + tan|-|| log|-1 + tan |-| - tan|-||
\ \8/ \8// \ \8/ \8//
- -------------------------- + --------------------------
4 4
$$\frac{\log{\left(\tan^{2}{\left(\frac{p}{8} \right)} - \tan{\left(\frac{p}{8} \right)} - 1 \right)}}{4} - \frac{\log{\left(\tan^{2}{\left(\frac{p}{8} \right)} + \tan{\left(\frac{p}{8} \right)} - 1 \right)}}{4}$$
=
=
/ 2/p\ /p\\ / 2/p\ /p\\
log|-1 + tan |-| + tan|-|| log|-1 + tan |-| - tan|-||
\ \8/ \8// \ \8/ \8//
- -------------------------- + --------------------------
4 4
$$\frac{\log{\left(\tan^{2}{\left(\frac{p}{8} \right)} - \tan{\left(\frac{p}{8} \right)} - 1 \right)}}{4} - \frac{\log{\left(\tan^{2}{\left(\frac{p}{8} \right)} + \tan{\left(\frac{p}{8} \right)} - 1 \right)}}{4}$$
-log(-1 + tan(p/8)^2 + tan(p/8))/4 + log(-1 + tan(p/8)^2 - tan(p/8))/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.