sec tan x  Now sec5 x tan x = secx tan xdx . dx Let u = sec x du = sec x tan xdx 5 5  Then c  5  sec = c  5 u Example 9 Find sin38x cos 8xdx du Let u = sin 8x, dx = 8 cos 8x du = 8 cos 8xdx 1 Then sin38x cos 8xdx = 8 3 1 = u3du u 4  32  c sin 8x 4  32  c 3.5 Integration of tan x and cot x (formulae) sinx a) tan  xdx cos dx du Let u = cosx, dx = -sinx, = -sinx dx, du 30 cos tan  xdx Then - dx
5  sec tan x Now sec5 x tan x dx = secx tan xdx . Let u = sec x du = sec x tan xdx Then sec 5 = u   c 5   c 5 Example 9 Find sin38x cos 8xdx Let u = sin 8x, du dx = 8 cos 8x du = 8 cos 8xdx Then sin38x cos 8xdx = 1 8 3 = 1 u3du  u 4 32  c  sin 4 8x 32  c 3.5 Integration of tan x and cot x (formulae) a) tan xdx  sinx cos dx Let u = cosx, du dx = -sinx, du = -sinx dx, 30 Then tan xdx  - cos dx
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