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Evaluate: intx/((sqrt(x^2+a^2)+sqrt(x^2-...

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

Text Solution

Verified by Experts

Let,`(x^2-a^2)=t^2`
=`xdx=tdt`
I=`intx/(x^2+a^2.sqrt(x^2-a^2))dx`
=`int t/(t^2+a^2+a^2.sqrt(t^2))dt`
=`int 1/(t^2+2a^2).dt`
=`int 1/(t^2+sqrt(2a)^2).dt`
...
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