Why the integral of $2 \cdot \frac{\ln(x)}{x}$ is $\ln(x)^2 + C$ (where $C$ is of course a constant) ?
After some years of my high school math classes, I am again doing derivatives and integrals, but I am confused again.
I am not seeing why exactly the integral of $\int{2 \cdot \frac{\ln(x)}{x}} dx$ is $\ln(x)^2 + C$. Apparently, it has used the chain rule, which should be (if I am not wrong) the rule for deriving composition of functions, but I am not seeing where and how the chain rule can be applied backwards to find the anti derivative.
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