integration by completion of squares

Integration by completion of squares

Integration formulae

If an integral is of

sqrt(ax² + bx +c) , 1 /sqrt(ax² + bx +c) ,1 /(ax² + bx +c) type

first complete the square

ax² + bx +c = a[ x² + (b/a)x + (c/a) ] =a[ ( x +(b/2a) )² + (c/a) -(b²/4a²) ]

remember to make the coefficient of x² unity before starting
Examples on integration by completion of squares

* integral of [ 1 / (x² -x+1)]
integral using completion of squares method

*integral of 1 / sqrt[4 + 3x - x² ]
completion of squares inside a square root

PAGE 1 BASIC INTEGRATION
PAGE 2 INTEGRATION BY SUBSTITUTIONPAGE 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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