$\cfrac{{{{\left( {1 + \log x} \right)}^2}}}{x}$
$\cfrac{{{{\left( {1 + \log x} \right)}^2}}}{x}$
Official Solution
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NCERT & Exemplar
: Let $I = \int {\cfrac{{{{\left( {1 + \log x} \right)}^2}}}{x}} dx$
Put $1 + \log x = t$ $\Rightarrow$ $\cfrac{1}{x}dx = dt$
$\therefore$ $I = \int {{t^2}} dt = \cfrac{{{t^3}}}{3} + C = \cfrac{1}{3}{\left( {1 + \log x} \right)^3} + C$
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