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int(0)^(1)(logx)/(sqrt(1-x^(2)))dx=-(pi)...

`int_(0)^(1)(logx)/(sqrt(1-x^(2)))dx=-(pi)/(2)(log2)`

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To solve the integral \[ I = \int_{0}^{1} \frac{\log x}{\sqrt{1 - x^2}} \, dx, \] we will use a substitution and properties of logarithms and integrals. Let's go through the steps in detail. ...
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int_(0)^(1)(log x)/(sqrt(1-x^(2)))dx

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Knowledge Check

  • int_(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=

    A
    7
    B
    0
    C
    `5 log 13`
    D
    `2 log5`

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