Sr Examen
Integral de (cos(2x-(pi/4)))^(-2) dx
Solución
Ha introducido
[src]
1 / | | 1 | -------------- dx | 2/ pi\ | cos |2*x - --| | \ 4 / | / 0
$$\int\limits_{0}^{1} \frac{1}{\cos^{2}{\left(2 x - \frac{\pi}{4} \right)}}\, dx$$
Integral(cos(2*x - pi/4)^(-2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / 3*pi\ | cot|x + ----| | 1 \ 8 / | -------------- dx = C + ------------------- | 2/ pi\ 2/ 3*pi\ | cos |2*x - --| -1 + cot |x + ----| | \ 4 / \ 8 / | /
$$\int \frac{1}{\cos^{2}{\left(2 x - \frac{\pi}{4} \right)}}\, dx = C + \frac{\cot{\left(x + \frac{3 \pi}{8} \right)}}{\cot^{2}{\left(x + \frac{3 \pi}{8} \right)} - 1}$$
Gráfica
Respuesta
[src]
/ pi\
___ tan|1 + --|
1 \/ 2 1 1 \ 8 /
- - ----- - ------------- + -------------- + -----------
4 4 / pi\ / ___\ 4
4*tan|1 + --| 4*\-1 + \/ 2 /
\ 8 /
$$- \frac{\sqrt{2}}{4} - \frac{1}{4 \tan{\left(\frac{\pi}{8} + 1 \right)}} + \frac{1}{4} + \frac{1}{4 \left(-1 + \sqrt{2}\right)} + \frac{\tan{\left(\frac{\pi}{8} + 1 \right)}}{4}$$
=
=
/ pi\
___ tan|1 + --|
1 \/ 2 1 1 \ 8 /
- - ----- - ------------- + -------------- + -----------
4 4 / pi\ / ___\ 4
4*tan|1 + --| 4*\-1 + \/ 2 /
\ 8 /
$$- \frac{\sqrt{2}}{4} - \frac{1}{4 \tan{\left(\frac{\pi}{8} + 1 \right)}} + \frac{1}{4} + \frac{1}{4 \left(-1 + \sqrt{2}\right)} + \frac{\tan{\left(\frac{\pi}{8} + 1 \right)}}{4}$$
1/4 - sqrt(2)/4 - 1/(4*tan(1 + pi/8)) + 1/(4*(-1 + sqrt(2))) + tan(1 + pi/8)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.