Find ∫sin2xdx.
Solution Since the exponent of sinx is an even integer, we use the identity sin2x=1−cos(2x)2
Then ∫sin2xdx=12∫[1−cos(2x)]dx=12∫dx−12∫cos(2x)dx=12x+C1−12∫cosudu2u=2x,du=2dx.=12x+C1−14sin(2x)+C2
482
Since C1 and C2 are constants, we write the solution as ∫sin2xdx=12x−14sin(2x)+C
where C=C1+C2.