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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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