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If int x((ln(x+sqrt(1+x^2)))/sqrt(1+x^2)...

If `int x((ln(x+sqrt(1+x^2)))/sqrt(1+x^2)) dx=asqrt(1+x^2)ln(x+sqrt(1+x^2))+bx+c` then

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If int(xln(x+sqrt(1+x^2)))/(sqrt(1+x^2))dx =asqrt(1+x^2)ln(x+sqrt(1+x^2))+b x+c , then (A) a=1,b =-1 (B) a=1,b=1 (C) a=-1, b=1 (D) a=-1, b=-1

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Knowledge Check

  • int(log(x+sqrt(1+x^(2))))/(sqrt(1+x^(2)))dx=

    A
    `1/2[log(x+sqrt(1+x^(2)))]^(2)+c`
    B
    `log(x+sqrt(1+x^(2)))^(2)+c`
    C
    `log(x+sqrt(1+x^(2)))+c`
    D
    None of these

  • int(log(x+sqrt(1+x^(2))))/(sqrt(1+x^(2)))dx=....+c

    A
    `(1)/(2)[log(x+sqrt(1+x^(2)))]^(2)`
    B
    `log[x+sqrt(1+x^(2))]^(2)`
    C
    `log(x+sqrt(1+x^(2)))`
    D
    None of these

  • If int(log(x+sqrt(1+x^(2))))/(sqrt(1+x^(2)))dx =(gof)(x)+c then

    A
    `f(x)=log(x+sqrt(x^(2)+1))and g(x)=k`
    B
    `f(x)=log(x+sqrt(x^(2)+1))and g(x)=x^(2)`
    C
    `f(x)=log(x+sqrt(x^(2)+1))and g(x)=(x^(2))/(2)`
    D
    `g(x)=log(x+sqrt(x^(2)+1))and f(x)=(x^(2))/(2)`

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