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If int(sqrt(cotx))/(sinxcosx)dx=Psqrt(co...

If `int(sqrt(cotx))/(sinxcosx)dx=Psqrt(cotx)+Q` , then P equals

A

1

B

2

C

`-1`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `I=int(sqrt(cotx))/(sinxcosx)dx`
`rArrI=int(sqrt(cotx))/(tanx)sec^(2)xdx` " " `["Dividing"N^(r)and D^(r)"by "cos^(2)x]`
`rArrI=int(tanx)^(-3//2)d(tanx)`
`rArrI=-2(tanx)^(-1//2)+Q=-2sqrt(cot)x+Q`
Hence , P =-2
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