Evaluate: `intx\ sqrt((a^2-x^2)/(a^2+x^2))\ dx`

Explanation

Given,

`intx\ sqrt((a^2-x^2)/(a^2+x^2))\ dx`

let `x^2=t`

`2xdx=dt`

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

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

=`1/2 [int a^2/sqrt(a^4-t^2)dt-int t/sqrt(a^4-t^2)dt]`

Let`a^4-t^2=u`

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