How do you integrate $\frac{ln x}{x}$ $ln x / x$ ?

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How do you integrate $\frac{ln x}{x}$ $ln x / x$ ?

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Answer 1 · 2016-05-01T04:47:41

Remember that $d \frac{ln x}{d x} = \frac{1}{x}$ $d(lnx)/dx=1/x$ hence

$\int (\frac{1}{x}) \cdot ln x d x = \int (d \frac{ln x}{d x}) \cdot ln x \cdot d x = \frac{1}{2} \cdot \int (d \frac{{(ln x)}^{2}}{d x}) \cdot d x = \frac{1}{2} \cdot {(ln x)}^{2} + c$ $int (1/x)*lnxdx=int (d(lnx)/dx)*lnx*dx= 1/2*int (d(lnx)^2/dx)*dx=1/2*(lnx)^2+c$

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How do you integrate $\frac{ln x}{x}$ $ln x / x$ ?

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