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Find : int(sqrt(x^2+1)(log(x^2+1)-2logx)...

Find : `int(sqrt(x^2+1)(log(x^2+1)-2logx)/(x^4)dx`

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int(sqrt(x^(2)+1)(log(x^(2)+1)-2log x))/(x^(4))dx

Evaluate int sqrt(x^(2)+1)(log(x^(2)+1)-2log x)/(x^(4))dx

Knowledge Check

  • int(sqrt(x^2+1)[log(x^2+1)-2logx])/(x^4) dx is equal to

    A
    `1/3 (1+1/x^2)^(1//2)[log(1+1/x^2)+2/3]+c`
    B
    `-1/3 (1+1/x^2)^(3//2)[log(1+1/x^2)-2/3]+c`
    C
    `2/3 (1+1/x^2)^(3//2)[log(1+1/x^2)+2/3]+c`
    D
    none of these

  • int(sqrt(x^(2)+1)[log(x^(2)+1)-2logx])/(x^(4)) dx is equal to

    A
    `(1)/(3)(1+(1)/(x^(2)))^(1//2)[log(1+(1)/(x^(2)))+(2)/(3)]+C`
    B
    `(1)/(3)(1+(1)/(x^(2)))^(3//2)[log(1+(1)/(x^(2)))-(2)/(3)]+C`
    C
    `(2)/(3)(1+(1)/(x^(2)))^(3//2)[log(1+(1)/(x^(2)))+(2)/(3)]+C`
    D
    none of these

  • int(sqrt((x^2+1))[log(x^2+1)-2logx])/x^4dx is equals to

    A
    `1/3(1+1/x^2)^(1//2)[log(1+1/x^2)+2/3]+C`
    B
    `-1/3(1+1/x^2)^(3//2)[log(1+1/x^2)-2/3]+C`
    C
    `2/3(1+1/x^2)^(3//2)[log(1+1/x^2)-2/3]+C`
    D
    None of the above

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