int(1)/(tanx+cotx+secx+"cosec "x)dx is e...

`int(1)/(tanx+cotx+secx+"cosec "x)dx` is equal to

A

`(1)/(2)(sinx+cosx+x)+C`

B

`(1)/(2)(sinx-cosx-x)+C`

C

`(1)/(2)(cosx-xsinx)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

d

Let `=int(1)/(tanx+cotx+secx+"cosec " x)dx` Then ,
`I=int(sinxcosx)/(1+sinx+cosx)dx`
`rArrI=(1)/(2)int((1+2sinx cosx-1))/(1+sinx+cosx)dx=(1)/(2)int((sinx+cosx)^(2)-1)/(1+sinx+cosx)`
`rArr I=(1)/(2)int((sinx+cosx+1)(sinx+cosx-1))/(1+sinx+cosx)dx`
`rArr I=(1)/(2)int(sinx+cosx-1)dx`
`rArrI=(1)/(2)(-cosx+sinx-1)+C`

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int(dx)/(tanx+cotx+secx+cos e c x)=

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Knowledge Check

int cosec (x-a) cosec x dx is equal to

A

`-1/sina log [sinx coses (x -a)sin x]+C`

B

`-1/sina log [sin(x-a)sinx]+C`

C

`1/sina log [sin(x-a) cosec x]+C`

D

`1/sina log [sin(x-a)sinx]+C`

The given expression f(x)=(1)/(tanx+cotx+secx+"cosec x") is equivalent to

A

`(1)/(2(sinx+cosx-1))`

B

`(sinx+cosx-1)/(2)`

C

`(1)/(2(sinx-cosx+1))`

D

`(sinx-cosx+1)/(2)`

The expression (1)/(tanx+cotx+secx+"cosec x") equivalent to

A

`(1)/(2(sinx+cosx-1))`

B

`((sinx+cosx-1))/(2)`

C

`(1)/(2(sinx-cosx+1))`

D

`((sinx-cosx+1))/(2)`

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