integral of { [ arcsin(sqrt(x)) - arccos(sqrt(x)) ] / [ arcsin(sqrt(x)) + arccos(sqrt(x))] }

x belongs to [0,1]

use the result that arcsin(sqrt(x)) + arccos(sqrt(x))] = [pi / 2]

to get rid of arccos(sqrt(x)) and write the integral completely in terms of arcsin(sqrt(x))

use a substitution to change the arc sine function to a function involving sine function

use integration by parts to handle the new integral.

formulae on integration

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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