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