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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`

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To solve the integral \( \int \frac{dx}{x(1+x^2)} \), we can use substitution and partial fraction decomposition. Here’s a step-by-step solution: ### Step 1: Rewrite the Integral We start with the integral: \[ \int \frac{dx}{x(1+x^2)} \] ...
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