5.4 Integration the fundamental identities Sin2 x + cos2 x = 1 (1) 1 + tan2 x = sec2 x (2) 2 Example 1 Find sin2 x 1 cos  Solution Using the identity (1) sin x + cos2 x = 1 2 sin2 (1 cos2 x x) (1 cos  cos x)(1 = dx (1 cos  x) = (1 cos x)dx = x sin x + c – Example 2 2 Find xdx 43 Solution We use 1 + tan2 x = sec2 x Then (sec xdx x = 2 2 2 = tan x x + c – Example 3 cos2 x Find 1 sin x
5.4 Integration the fundamental identities Sin2 x + cos2 x = 1 (1) 1 + tan2 x = sec2 x (2) 2 Example 1 Find sin2 x 1  cos Solution Using the identity (1) sin 2 x + cos2 x = 1 sin2 x (1 cos2 x) = (1 cos x)(1  cos (1  cos x) dx = (1 cos x)dx = x – sin x + c Example 2 Find 2 xdx 43 Solution We use 1 + tan2 x = sec2 x Then 2 xdx = (sec 2 x 2 = tan x – x + c Example 3 Find cos2 x 1 sin x
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