1 / | | 1 | -------- dx | cos(5*x) | / 0
Integral(1/cos(5*x), (x, 0, 1))
/ | | 1 | -------- dx | cos(5*x) | /
1 -------- cos(5*x)
cos(5*x)
1 cos(5*x) -------- = --------- cos(5*x) 2 cos (5*x)
sin(a)^2 + cos(a)^2 = 1
2 2 cos (5*x) = 1 - sin (5*x)
cos(5*x) cos(5*x) --------- = ------------- 2 2 cos (5*x) 1 - sin (5*x)
u = sin(5*x)
/ | | cos(5*x) | ------------- dx | 2 = | 1 - sin (5*x) | /
/ | | cos(5*x) | ------------- dx | 2 = | 1 - sin (5*x) | /
/ | | 1 | ---------- du | / 2\ | 5*\1 - u / | /
1 1 / 1 1 \ ---------- = ---*|----- + -----| / 2\ 5*2 \1 - u 1 + u/ 5*\1 - u /
/ / | | | 1 | 1 | ----- du | ----- du / | 1 + u | 1 - u | | | | 1 / / = | ---------- du = ----------- + ----------- | / 2\ 10 10 | 5*\1 - u / | /
= -log(-1 + u)/10 + log(1 + u)/10
u = sin(5*x)
/ | | 1 log(-1 + sin(5*x)) log(1 + sin(5*x)) | -------- dx = - ------------------ + ----------------- + C0 | cos(5*x) 10 10 | /
/ | | 1 log(-1 + sin(5*x)) log(1 + sin(5*x)) | -------- dx = C - ------------------ + ----------------- | cos(5*x) 10 10 | /
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.