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int x (log x)^(2)dx...

`int x (log x)^(2)dx`

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To solve the integral \( \int x (\log x)^2 \, dx \), we will use integration by parts, applying the ILATE rule (Inverse, Logarithmic, Algebraic, Trigonometric, Exponential) to choose our functions. ### Step-by-step Solution: 1. **Identify the functions**: - Let \( u = (\log x)^2 \) (Logarithmic function) - Let \( dv = x \, dx \) (Algebraic function) ...
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