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# Evaluate : $\int\large\frac{(log\: x)^2}{x} $$dx Can you answer this question? ## 1 Answer 0 votes Toolbox: • Method of substitution : • Given f(x)dx can be transformed into another form by changing independent variable x to t by substituting x=g(t). • Consider I=\int f(x)dx. • Put x=g(t) so that \large\frac{dx}{dt}$$=g'(t).$
• $\Rightarrow$dx=g'(t)dt.
• Thus $I=\int f(g(t).g'(t))dt.$
Step 1:
$I=\int\large\frac{(\log x)^2}{x}$$dx Let \log x=t On differentiating we get, I=\int t^2dt Step 2: On integrating we get, I=\large\frac{t^3}{3}$$+c$
Substituting for $t$ we get,