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int(dx)/(cos(2x)cos(4x))=...

`int(dx)/(cos(2x)cos(4x))=`

A

`(1)/(2sqrt2)log|(1+sqrt2sin2x)/(1-sqrt2sin2x)|-(1)/(2)(log|sec2x-tan2x|)+C`

B

`(1)/(2sqrt2)log|(1-sqrt2sin2x)/(1+sqrt2sin2x)|-(1)/(2)(log|sec2x-tan2x|)+C`

C

`(1)/(sqrt2)log|(1+sqrt2sin2x)/(1-sqrt2sin2x)|-(1)/(2)(log|sec2x-tan2x|)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`int(sin(4x-2x)dx)/(sin(2x)cos(2x)cos(4x))`
`=int(sin(4x)dx)/(sin(2x)cos(4x))-int sec2xdx`
`=2int(cos2xdx)/(cos4x)-(1)/(2)(log|sec 2x-tan 2x|)`
`=2int(cos2xdx)/(1-2sin^(2)2x)-(1)/(2)(log|sec2x-tan2x|)`
`=int(dt)/(1-2t^(2))-(1)/(2)(log|sec 2x-tan2x|)`
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CENGAGE-INDEFINITE INTEGRATION-Single Correct Answer Type
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