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If l=intsec^2xcos e c^4x dx=Acot^3x+Btan...

If `l=intsec^2xcos e c^4x dx=Acot^3x+Btanx+Ccotx+D ,` then `A=-1/3` (b) `B=2` `C=-2` (d) none of these

A

`A=-(1)/(3)`

B

`B=2`

C

`C=-2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, C
`I=int sec^(2)x "cosec"^(4)xdx`
`=int((sin^(2)x+cos^(2)x)^(2))/(cos^(2)xsin^(4)x)dx`
`=int(sin^(4)x+cos^(4)x+2sin^(2)x cos^(2)x)/(cos^(2)xsin^(4)x)dx`
`=int(sec^(2)x+2"cosec"^(2)x+(cos^(2)x)/(sin^(4)x))dx `
`=tanx-2cotx+int cot^(2)x"cosec"^(2)x dx`
`=tanx-2cotx-(cot^(3)x)/(3)+D`
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