integral of 1 / sqrt[4 + 3x - x² ] using completion of squares method

integral of 1 / sqrt[4 + 3x - x² ] using completion of squares method

integrate after completing the square
to make the coefficient of x²  (+1) , take -1 common , but it remains inside the sqrt sign
to get sqrt [ - ( x² -3x - 4)] now take half the coefficient of x , that is half of (-3)
to get [x- (3/2) ]² and then adjust the constant term and finally re introduce the -1 taken  out earlier

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION 

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

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