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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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  13. If sqrt(x+sqrt(x^(2)+x))dx=A{x+sqrt(x^(2)+2)}^(3//2)+(B)/(sqrt(x+sqrt(...

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  14. int(x^(2)+1)/(xsqrt(x^(2)+2x-1)sqrt(1-x^(2)-x))dx is equal to

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  15. int(dx)/(x^(2)sqrt(16-x^(2))) has the value equal to

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  16. If int(3tan(x-(pi)/(4)))/(cos^(2)xsqrt(tan^(3)x)+tan^(2)x+tanx)=Ktan^(...

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  17. int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

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