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EXAMPLE 3Finding an Integral Containing 2xx2

Find dx2xx2.

Solution The integrand contains the quadratic expression 2xx2, so we complete the square. 2xx2=x2+2x=(x22x)=(x22x+1)+1=(x1)2+1=1(x1)2

Then dx2xx2=dx1(x1)2=u=x1du=dxdu1u2=sin1u+C=sin1(x1)+C