Write an anti-derivative for the following fu | vedclass

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(A) We know that the derivative of $\log x$ with respect to $x$ is $\frac{1}{x}$ for $x > 0$. Also,for $x < 0$,let $y = -x$,then $\frac{d}{dx}(\log(-x

Vedclass · Accepted Answer

$\log |x|$

Vedclass · Answer

(A) We know that the derivative of $\log x$ with respect to $x$ is $\frac{1}{x}$ for $x > 0$. Also,for $x Combining these two cases,we get $\frac{d}{dx}(\log |x|) = \frac{1}{x}$ for all $x 
eq 0$. By the definition of an anti-derivative,if $\frac{d}{dx}(F(x)) = f(x)$,then $F(x)$ is an anti-derivative of $f(x)$. Therefore,$\log |x|$ is an anti-derivative of $\frac{1}{x}$.

Write an anti-derivative for the following function using the method of inspection: $\frac{1}{x}, x \neq 0$

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