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EXAMPLE 2Finding the Integral sin2xdx

Find sin2xdx.

Solution Since the exponent of sinx is an even integer, we use the identity sin2x=1cos(2x)2

Then sin2xdx=12[1cos(2x)]dx=12dx12cos(2x)dx=12x+C112cosudu2u=2x,du=2dx.=12x+C114sin(2x)+C2

482

Since C1 and C2 are constants, we write the solution as sin2xdx=12x14sin(2x)+C

where C=C1+C2.