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Integral of x dx / sqrt(x+2)
Make the substitution sqrt(x+2)=u
(x+2)^(1/2) = u
(1/2)(x+2)^(-1/2) dx = du
1/2(x+2)^(1/2) dx = du
1/2sqrt(x+2) dx = du
1/sqrt(x+2) dx = 2 du
Integral of x dx / sqrt(x+2) = Integral 2 x du
sqrt(x+2) = u
(x+2)=u^2
x=u^2-2
Integral 2 x du = Integral 2(u^2-2) du
= Integral 2u^2 du - 4 du
= 2 u^3/3 - 4u + C
= (2/3) (x+2)^(3/2) - 4 sqrt(x+2) + C
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