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