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If int(cos4x+1)/(cotx-tanx)dx = Acos4x+B...

If `int(cos4x+1)/(cotx-tanx)dx = Acos4x+B ,t h e n` (a)`A=-1/8` (b) `B=1/2` (c) `A=-1/4` (d) None of this

A

`A=-1//2`

B

`A=-1//8`

C

`A=-1//4`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`int(cos4x+1)/(cotx-tanx)dx=int(2cos^(2)2x)/(cos^(2)x-sin^(2)x)sinx cosx dx`
`=int cos2x sin2x dx`
`=(1)/(4)int sin4xdx=-(1)/(8)cos4x+C`
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