# Math Help - help needed integral [1 to 2] (lnx)^2/(x^3)

1. ## help needed integral [1 to 2] (lnx)^2/(x^3)

integral [1 to 2] (lnx)^2/(x^3)

how would i solve this

2. Originally Posted by kensington
integral [1 to 2] (lnx)^2/(x^3)

how would i solve this
integration by parts? where u= (ln x)^2 and v=1/x^3

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3. $\int \frac{(ln(x))^2}{x^3}dx$

When I see a ln(x) and an x in the denominator, the first thing I think of is to substitute u= ln(x). Then $du= \frac{1}{x} dx$. In this problem that still leaves $x^2$ in the denominator but if u= ln(x), then $x= e^u$ and $\frac{1}{x^2}= e^{-2u}$.

The integral becomes $\int ue^{-2u}du$ which can be done by integration by parts.