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Evaluate: int(sinx)/(sqrt(4cos^2x-1))\ d...

Evaluate: `int(sinx)/(sqrt(4cos^2x-1))\ dx`

Text Solution

Verified by Experts

I=`int(sinx)/(sqrt(4cos^2x-1))\ dx`
let `cosx=t`
`-sinxdx=dt`
I=-`int(dt)/(sqrt((sqrt(2)t)^2-1))`
`I=--1/sqrt(2) ``int(dt)/(sqrt((t)^2-1/(sqrt(2)))`
`I=--1/sqrt(2)sin^(-1)(t/(1/(sqrt(2))))`
`I=--1/sqrt(2)sin^(-1)((cosx)/(1/(sqrt(2))))+c ...
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