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Evaluate: inttan^(-1)sqrt((1-x)/(1+x))dx...

Evaluate: `inttan^(-1)sqrt((1-x)/(1+x))dx`

Text Solution

Verified by Experts

The correct Answer is:
`theta cos 2 theta-(sin2 theta)/(2)+C`
` I=int tan^(-1)sqrt((1-x)/(1+x))dx`
` "Let "x=cos2 theta " or "dx=-2sin2 theta d theta `
`:. I=int tan^(-1)sqrt((1-cos2 theta)/(1+cos2 theta))(-2sin2 theta)d theta `
`=-2int tan^(-1)(tan theta)sin2 theta d theta `
`=-2int theta sin 2 theta d theta `
`=-2[-(theta cos2 theta)/(2)+int(cos2 theta)/(2) d theta]`
`=theta cos 2 theta-(sin2 theta)/(2)+C`
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