How do I evaluate the integral $\int \frac{ln (2 x)}{x^{2}} d x$ $intln(2x)/ x^2 dx$ ?

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How do I evaluate the integral $\int \frac{ln (2 x)}{x^{2}} d x$ $intln(2x)/ x^2 dx$ ?

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Answer 1 · 2015-01-28T19:41:19

I would use integration by parts and the fact that:
$\frac{1}{x^{2}} = x^{- 2}$ $1/x^2=x^-2$ ;
derivative of $ln (2 x)$ $ln(2x)$ is: $\frac{2}{2 x} = \frac{1}{x}$ $2/(2x)=1/x$ (Chain Rule);
and $\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + c$ $intx^ndx=x^(n+1)/(n+1)+c$

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How do I evaluate the integral $\int \frac{ln (2 x)}{x^{2}} d x$ $intln(2x)/ x^2 dx$ ?

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How do I evaluate the integral $\int \frac{ln (2 x)}{x^{2}} d x$ $intln(2x)/ x^2 dx$ ?