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int tan^(-1)((cosx-sin x)/(cosx+sinx))dx...

`int tan^(-1)((cosx-sin x)/(cosx+sinx))dx` is equal to

A

`pi/4 x-x^2/2+C`

B

`pi/4 x + x^3/3+C`

C

`pi/5 x- x^2/2+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
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Knowledge Check

  • int(1)/(cosx-sinx)dx is equal to

    A
    `(1)/(sqrt(2))log|tan((x)/(2)+(3pi)/(8))|+C`
    B
    `(1)/(sqrt(2))log|"cot"(x)/(2)|+C`
    C
    `(1)/(sqrt(2))log|tan((x)/(2)-(3pi)/(8))|+C`
    D
    `(1)/(sqrt(2))log|tan((x)/(2)-(pi)/(8))|+C`
  • int (dx)/(1-cosx-sin x) is equal to

    A
    `log|1+ "cot"x/2|+C`
    B
    `log|1-"tan" x/2|+C`
    C
    `log |1-"cot" x/2| +C`
    D
    `log|1+"tan" x/2| +C`
  • int(cosx-sinx)/(1+2sin x cosx)dx is equal to

    A
    `-(1)/(cos x- sinx)+C`
    B
    `(cos x+sin x)/(cos x-sinx)+C`
    C
    `-(1)/(sin x+cosx)+C`
    D
    `(x)/(sinx+cosx)+C`
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