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√((1+x)/(1-x)).DXWhat`s the solution of this and what`s the answer.

√((1+x)/(1-x)).DXWhat`s the solution of this and what`s the answer.

Grade:12th pass

1 Answers

Aswath
11 Points
6 years ago
Substitute x=cos 2t.(1+cos2t/1-cos2t)^1/2.Now expand cos2t as (cost)^2-(sint)^2and expand 1 as sint^2+cost^2This gives cost/sint.dx.Cos t is the derivative of sint.Let sint be u.Now it becomes (1/u).duIntegrating it it gives ln u=ln sint.X=cos 2tX=(cos t)^2-(sint )^2.This can be expressed as1-x=1-((cost)^2-(sint)^2)1-x=2(sint)^2Sint =(1-x/2)^1/2.ln u=ln((1-x)/2)/2..

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