3.5.2—Trig integration

Rewrite products or powers of sin and cos using identities, then integrate each term. For an inner multiple angle, include the reciprocal derivative factor.

For even powers use half-angle identities; for odd powers save one factor and substitute. Keep absolute values in logarithmic results.

∫cos²x dx=x/2+sin2x/4+C; ∫sin(4x)dx=−cos(4x)/4+C.

A power on sin or cos is not an instruction to raise its antiderivative to a power.