Evaluate : int(logx)/(x^(2))dx....

Evaluate : `int(logx)/(x^(2))dx`.

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To evaluate the integral \( \int \frac{\log x}{x^2} \, dx \), we will use the method of integration by parts. ### Step 1: Identify \( u \) and \( dv \) We choose: - \( u = \log x \) (which we will differentiate) - \( dv = \frac{1}{x^2} \, dx \) (which we will integrate) ### Step 2: Differentiate \( u \) and Integrate \( dv \) ...

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int(logx)/(x^3)dx=

`(1)/(4x^2)(2logx-1)+c`

`(-1)/(4x^2)(2logx+1)+c`

`(1)/(4x^2)(2logx+1)+c`

`(1)/(4x^2)(1-2logx)+c`

int(logx)/(x+1)^2dx=

`(-logx)/(x+1)+log|x|-log|x+1|+c`

`(logx)/(x+1)-log|x|-log|x+1|+c`

`(logx)/(x+1)+log|x|-log|x+1|+c`

`(-logx)/(x+1)-log|x|-log|x+1|+c`

int(logx)/x^2dx =

`1/x(logx+1)`

`-1/x (log x+1)`

`1/x (log x-1)`

`log (x+1)`