integral of 1 / { x*sqrt[ax-x^2]} using substitution

 integral of 1 / { x*sqrt[ax-x^2]} using substitution

method is put x = (a/t) ; dx = [-a / (t^2) ] dt

replace x and dx in the given equation and simplify as shown below

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


PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

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