Evaluate the following integral: `int_(-a)^asqrt((a+x)/(a-x))dx`

Explanation

Let `I=int_(-a)^asqrt((a+x)/(a-x))dx`

put,`x=acos2y⇒dx=−2asin2ydy`.


=`int_(-a)^asqrt((a+acos2y)/(a-acos2y))dx`

`I_1=∫(coty)(−2asin2y)dy.`

`=−2a∫2cos^2ydy`


`=−2a∫(1+cos2y)dy`

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