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

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

disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work