વિધેય $\frac{x}{\sqrt{x+4}}, x > 0$ નું સંકલન કરો.

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ધારો કે $x+4 = t$.
તેથી $dx = dt$ અને $x = t-4$.
આ કિંમતો સંકલનમાં મૂકતા:
$\int \frac{x}{\sqrt{x+4}} dx = \int \frac{t-4}{\sqrt{t}} dt$
$= \int \left( \frac{t}{\sqrt{t}} - \frac{4}{\sqrt{t}} \right) dt$
$= \int (t^{1/2} - 4t^{-1/2}) dt$
$= \frac{t^{3/2}}{3/2} - 4 \left( \frac{t^{1/2}}{1/2} \right) + C$
$= \frac{2}{3} t^{3/2} - 8 t^{1/2} + C$
$= \frac{2}{3} t^{1/2} (t - 12) + C$
હવે $t = x+4$ પાછા મૂકતા:
$= \frac{2}{3} \sqrt{x+4} (x+4-12) + C$
$= \frac{2}{3} \sqrt{x+4} (x-8) + C$,જ્યાં $C$ એ સ્વૈર અચળાંક છે.

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