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Evaluate the following integrals : intsi...

Evaluate the following integrals : `intsin^(-1)((2tanx)/(1+tan^2x))dx`

Text Solution

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We have given,
`intsin^(-1)((2tanx)/(1+tan^2x))dx` Let
` I=int sin ^{-1}(frac{2 tan x}{1+tan ^{2} x}) d x`
We know `sin 2 theta=frac{2 tan theta}{1+tan ^{2} theta}`
Therefore, we can write the integral as
`I=int sin ^{-1}(sin 2 x) d x`
`implies I=int 2 x d x`
...
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