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EXAMPLE 3Using Properties of the Indefinite Integral

  1. (a) (12x5+1x)dx=121x5dx+1xdx=12x5dx+x1/2dx=12(x44)+x1/212+C=3x4+2x+C
  2. (b) x2+6x2+1dx=Algebra(x2+1)+5x2+1dx=[x2+1x2+1+5x2+1]dx=[1+5x2+1]dx=Sum Propertydx+5x2+1dx=dx+51x2+1dx=x+5tan1x+C