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If intsqrt((1-x)/(1+x))(dx)/x=log ((sqr...

If `intsqrt((1-x)/(1+x))(dx)/x=log ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))+2f(x)+C` then

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Knowledge Check

  • d/(dx){Cot^(-1)""(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}

    A
    `1/(sqrt(1-x^2))`
    B
    `(-1)/(2(sqrt(1-x^2)))`
    C
    `(1)/(sqrt(1+x^2))`
    D
    `(-1)/(2(1+x^2))`

  • (d)/(d x ) { log (sqrt(1 +x )+ sqrt( 1 -x ))/(sqrt(1 + x ) - sqrt(1-x ))}=

    A
    `(1)/(x sqrt( 1 - x^(2)))`
    B
    `(-1)/(sqrt( 1 - x^(2)))`
    C
    `(-1)/(xsqrt( 1 - x^(2)))`
    D
    none

  • int((1+x)+sqrt(x)*sqrt(1+x))/(sqrt(x)+sqrt(1+x)))) dx is equal to

    A
    `1/2 sqrt(1+x)+c`
    B
    `2/3(1+x)^(3//2)+c`
    C
    `sqrt(1+x)+c`
    D
    `2(1+x)^(3//2)+c`

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    Evaluate : int(sqrt(x+1)-sqrt(x-1))/(sqrt(x+1)+sqrt(x-1))dx

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