2.5.2—Trig integration

Rewrite powers or products using identities such as sin²x=(1−cos2x)/2, then integrate term by term. If an inner angle is present, substitute it with its differential.

Use the identity that reduces the power or creates a derivative factor; keep absolute values in logarithmic antiderivatives such as ∫tan x dx=−ln|cos x|+C.

∫sin²x dx=x/2−sin2x/4+C, while ∫sec²(3x)dx=tan(3x)/3+C.

∫sin²x is not −cos³x/3; the power is on the function, not on its differential pattern.