Integral of sin²(x): x/2 − sin(2x)/4 + C
The integral of sin²(x) is x/2 − sin(2x)/4 + C. Uses the power-reduction identity; includes cos²x, sin²(3x) and definite integrals over [0, π].
Category: Integrals
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Integral of sec(x): ln|sec x + tan x| + C, Step by Step
The integral of sec(x) is ln|sec x + tan x| + C. See the multiply-by-(sec x + tan x) trick, a second method, csc x, and definite examples.
Integral of tan(x): −ln|cos x| + C Derivation
The integral of tan(x) is −ln|cos x| + C, or equivalently ln|sec x| + C. Step-by-step u-substitution, definite examples and tan²x.
Integral of ln(x): x ln x − x + C (Integration by Parts)
The integral of ln(x) is x·ln(x) − x + C. Full integration by parts derivation, a check by differentiation, definite integral examples and variations.