Mathematics

Integrate
$$(4x +2)\sqrt{x^{2}+x+1}   dx$$


SOLUTION
Let $$I=\int (4x+2)\sqrt{x^2+x+1}dx$$
Let $$x^2+x+1=t\implies (4x+2)dx=2dt$$
So, $$I=\int 2\sqrt t dt=\cfrac{2(t)^{3/2}}{(3/2)}+c$$
$$I=\cfrac{4}{3}t^{3/2}+c$$
So, $$I=\cfrac{4}{3}(\sqrt{1+x+x^2})^3+c$$
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Subjective Medium Published on 17th 09, 2020
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