3*dx/cos(7*x)
1 / | | 1 | 3*1*-------- dx | cos(7*x) | / 0
Integral(3*1/cos(7*x), (x, 0, 1))
/ | | 1 | 1*3*1*-------- dx | cos(7*x) | /
1 3*1*-------- cos(7*x)
cos(7*x)
1 3*cos(7*x) 3*1*-------- = ---------- cos(7*x) 2 cos (7*x)
sin(a)^2 + cos(a)^2 = 1
2 2 cos (7*x) = 1 - sin (7*x)
3*cos(7*x) 3*cos(7*x) ---------- = ------------- 2 2 cos (7*x) 1 - sin (7*x)
u = sin(7*x)
/ | | 3*cos(7*x) | ------------- dx | 2 = | 1 - sin (7*x) | /
/ | | 3*cos(7*x) | ------------- dx | 2 = | 1 - sin (7*x) | /
/ | | 3 | ---------- du | / 2\ | 7*\1 - u / | /
3 3*1/7 / 1 1 \ ---------- = -----*|----- + -----| / 2\ 2 \1 - u 1 + u/ 7*\1 - u /
/ / | | | 1 | 1 3* | ----- du 3* | ----- du / | 1 + u | 1 - u | | | | 3 / / = | ---------- du = ------------- + ------------- | / 2\ 14 14 | 7*\1 - u / | /
= -3*log(-1 + u)/14 + 3*log(1 + u)/14
u = sin(7*x)
/ | | 1 3*log(-1 + sin(7*x)) 3*log(1 + sin(7*x)) | 1*3*1*-------- dx = - -------------------- + ------------------- + C0 | cos(7*x) 14 14 | /
/ | | 1 3*log(-1 + sin(7*x)) 3*log(1 + sin(7*x)) | 3*1*-------- dx = C - -------------------- + ------------------- | cos(7*x) 14 14 | /
Use the examples entering the upper and lower limits of integration.