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int(dx)/(x(x^2+1)equal(A) log|x|-1/2log(...

`int(dx)/(x(x^2+1)`equal(A) `log|x|-1/2log(x^2+1)+C` (B) `log|x|+1/2log(x^2+1)+C`(C) `-log|x|+1/2log(x^2+1)+C`(D) `1/2log|x|+log(x^2+1)+C`

Text Solution

AI Generated Solution

To solve the integral \(\int \frac{dx}{x(x^2+1)}\), we can follow these steps: ### Step 1: Rewrite the Integral We start with the integral: \[ \int \frac{dx}{x(x^2+1)} \] We can rewrite this as: ...
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Knowledge Check

  • int (dx)/((x+1)(x-2))=A log (x+1)+B log (x-2)+C , where

    A
    `A+B=0`
    B
    `AB=0`
    C
    `A//B=-1`
    D
    None of these

  • If 2 log (x + 1) - log (x^2) -1) = log 2 . Then x equals to :

    A
    A)1
    B
    B)0
    C
    C)2
    D
    D)3