$\cfrac{{3{x^2}}}{{{x^6} + 1}}$
$\cfrac{{3{x^2}}}{{{x^6} + 1}}$
Official Solution
VVidaara Team
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NCERT & Exemplar
: Let $I = \int {\cfrac{{3{x^2}}}{{{x^6} + 1}}} dx$
Put ${x^3} = t$ $\Rightarrow$ $3{x^2}dx = dt$
$\therefore$ $I = \int {\cfrac{{dt}}{{{t^2} + 1}}} = {\tan ^{ - 1}}t + C = {\tan ^{ - 1}}\left( {{x^3}} \right) + C$
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