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Evaluate: int(1+tanx)/(1-tanx)dx...

Evaluate: `int(1+tanx)/(1-tanx)dx`

Text Solution

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We have given,
`int(1+tanx)/(1-tanx)dx`
`I=int(1+tan x)/(1-tan x)dx,`
`=int(1+(sin x)/(cos x))/(1-(sin x)/(cos x))dx,`
`=int(cos x+sin x)/(cos x-sin x)dx,`
Let ` cos x-sin x=t,`
`implies(-sin x-cos x)dx=dt,`
`implies(sin x+cos x)dx=-dt,`
...
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