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int (log (tanx))/(sin x cos x)dx=...

`int (log (tanx))/(sin x cos x)dx=`

A

`log^(2)(tan x)+c`

B

`(1)/(2) (log tanx)^(2)+c`

C

`log (log tan x)+c`

D

none

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • int (cos x)/( sin x log sin x)dx=

    A
    `log|sin x log sin x| +c`
    B
    `log| log sin x| +c`
    C
    `1//log sin x+c`
    D
    none

  • int (sin x)/(sin x + cos x) dx =

    A
    `(1)/(2) x + (1)/(2)` log | sin x + cos x | + C
    B
    `(1)/(2) x - (1)/(2) ` log | sin x + cos x |+ C
    C
    `(1)/(2)x` + log | sin x + cos x | + C
    D
    x - log |sin x + cos x | + C

  • int (1)/(sin x - cos x) dx =

    A
    `(1)/(sqrt(2)) log |tan ((x)/(2) - (pi)/(8)) | + c `
    B
    `(1)/(sqrt(3)) log |tan ((x)/(2) - (pi)/(8)) | + c `
    C
    `(1)/(sqrt(2)) log |tan ((x)/(2) + (pi)/(8)) | + c `
    D
    `(1)/(sqrt(2)) log |cos ((x)/(2) - (pi)/(8)) | + c `

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