Mathematics

Integrate the function 
$$x\sqrt {x+2}$$


SOLUTION
$$\int \sqrt {x+2}dx$$
put $$x+2=t\Rightarrow x  =t-2 $$

$$\displaystyle \int (t-2)\sqrt t (dt)$$

$$=\int ( t^{3/2}-2t^{1/2}) dt$$

$$=\dfrac {t^{5/2}}{5/2}-2 \times \dfrac {t^{3/2}}{3/2}=\dfrac 25 (x+2)^{5/2}-\dfrac 43 (x+2)^{3/2}+C$$
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Subjective Medium Published on 17th 09, 2020
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