$\cfrac{{4x + 1}}{{\sqrt {2{x^2} + x - 3} }}$
$\cfrac{{4x + 1}}{{\sqrt {2{x^2} + x - 3} }}$
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NCERT & Exemplar
: Let $I = \int {\cfrac{{4x + 1}}{{\sqrt {2{x^2} + x - 3} }}dx}$
Put $2{x^2} + x - 3 = t$ $\Rightarrow$ $\left( {4x + 1} \right)dx = dt$
$\therefore$ $I = \int {\cfrac{{dt}}{{\sqrt t }} = \int {{t^{1/2}}} } dt = 2{t^{1/2}} + C = 2\sqrt {2{x^2} + x - 3} + C$
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