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int(1+tan^2x)/(1-tan^2x)dx...

`int(1+tan^2x)/(1-tan^2x)dx`

A

`log((1-tanx)/(1+tanx))+C`

B

`log((1+tanx)/(1-tanx))+C`

C

`(1)/(2)log((1-tanx)/(1+tanx))+C`

D

`(1)/(2)log((1+tanx)/(1-tanx))+C`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l=int(1+tan^(2)x)/(1-tan^(2)x)dx=int(sec^(2)x)/(1-tan^(2)x)dx`
Put`" "tan x= t rArr sec^(2)x dx=dt`
` therefore" "l=int(dt)/(1-t^(2))=(1)/(2xx1)log((1+t)/(1-t))+C`
`=(1)/(2)log((1+tanx)/(1-tanx))+C`
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