Evaluate: `intsqrt((a-x)/(a+x))\ dx`

Explanation

Given,I=`intsqrt((a-x)/(a+x))\ dx`

=`intsqrt((a-x)/(a+x) xx (a-x)/(a-x))\ dx`

=`intsqrt((a-x)^2/(a^2-x^2) )\ dx`

=`int (a-x)/sqrt(a^2-x^2)dx`

=`a int dx/sqrt(a^2-x^2)-xint dx/sqrt(a^2-x^2)`

if `a^2-x^2=t`

`xdx=-dt/2`

=`a int dx/sqrt(a^2-x^2)+1/2int dt/sqrt(t)`

...