Sr Examen
Integral de (dx)/(cos^2(ax+b)) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------- dx | 2 | cos (a*x + b) | / 0
$$\int\limits_{0}^{1} \frac{1}{\cos^{2}{\left(a x + b \right)}}\, dx$$
Integral(1/(cos(a*x + b)^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / -pi \\
|| zoo*x for And|a = 0, b = ----||
|| \ 2 /|
|| |
|| x |
|| ------- for a = 0 |
|| 2 |
|| cos (b) |
/ || |
| || / pi\ |
| 1 || -|b + --| |
| ------------- dx = C + |< \ 2 / |
| 2 || zoo*x for a = ---------- |
| cos (a*x + b) || x |
| || |
/ || /b a*x\ |
|| -2*tan|- + ---| |
|| \2 2 / |
||-------------------- otherwise |
|| 2/b a*x\ |
||-a + a*tan |- + ---| |
|| \2 2 / |
\\ /
$$\int \frac{1}{\cos^{2}{\left(a x + b \right)}}\, dx = C + \begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = - \frac{\pi}{2} \\\frac{x}{\cos^{2}{\left(b \right)}} & \text{for}\: a = 0 \\\tilde{\infty} x & \text{for}\: a = - \frac{b + \frac{\pi}{2}}{x} \\- \frac{2 \tan{\left(\frac{a x}{2} + \frac{b}{2} \right)}}{a \tan^{2}{\left(\frac{a x}{2} + \frac{b}{2} \right)} - a} & \text{otherwise} \end{cases}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.