int1/(1+tanx)\ dx=...

`int1/(1+tanx)\ dx=` `

Text Solution

Verified by Experts

`I=∫(1)/(1+tanx)dx`
Put,
`t=tanx`
`dt=sec^2xdx`
`dt=(1+tan^2x)dx`
Therefore,
`I=∫(1)/((t+1)(t^2+1))dt`
...

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Choose the correct answer of the given question int 1/(1+tanx) dx = ___ +c

A

log |sexc-tanx|

B

` 2sec^2 x/2`

C

log|x+sinx|

D

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int(1)/(tanx+cotx)dx=

A

`log(secx+cosx)+c`

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`2cos 2x+c`

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`-(1)/(2)cos 2x+c`

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`(1)/(2)sin^(2)x+c`

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A

`(1)/(sec)+c`

B

`secx+log(secx+tanx)+c`

C

`cosx+log(cosx-cotx)+c`

D

`log(secx)+c`

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