Sr Examen
Integral de 1/(cosx(1+cosx)) dx
Solución
Ha introducido
[src]
157 --- 200 / | | 1 | ------------------- dx | cos(x)*(1 + cos(x)) | / 0
$$\int\limits_{0}^{\frac{157}{200}} \frac{1}{\left(\cos{\left(x \right)} + 1\right) \cos{\left(x \right)}}\, dx$$
Integral(1/(cos(x)*(1 + cos(x))), (x, 0, 157/200))
Respuesta (Indefinida)
[src]
/ | | 1 / /x\\ /x\ / /x\\ | ------------------- dx = C - log|-1 + tan|-|| - tan|-| + log|1 + tan|-|| | cos(x)*(1 + cos(x)) \ \2// \2/ \ \2// | /
$$\int \frac{1}{\left(\cos{\left(x \right)} + 1\right) \cos{\left(x \right)}}\, dx = C - \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} - \tan{\left(\frac{x}{2} \right)}$$
Gráfica
Respuesta
[src]
/ /157\\ /157\ / /157\\
- log|1 - tan|---|| - tan|---| + log|1 + tan|---||
\ \400// \400/ \ \400//
$$- \tan{\left(\frac{157}{400} \right)} + \log{\left(\tan{\left(\frac{157}{400} \right)} + 1 \right)} - \log{\left(1 - \tan{\left(\frac{157}{400} \right)} \right)}$$
=
=
/ /157\\ /157\ / /157\\
- log|1 - tan|---|| - tan|---| + log|1 + tan|---||
\ \400// \400/ \ \400//
$$- \tan{\left(\frac{157}{400} \right)} + \log{\left(\tan{\left(\frac{157}{400} \right)} + 1 \right)} - \log{\left(1 - \tan{\left(\frac{157}{400} \right)} \right)}$$
-log(1 - tan(157/400)) - tan(157/400) + log(1 + tan(157/400))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.