Using substitution, integrate x(2 + x))^1/2 where u^2 = 2 + x
u2 = 2 + xx = u2 - 2dx/du = 2u
ʃ x(2 + x))1/2 dx= ʃ xu dx= ʃ u(u2 - 2) dx= ʃ 2u2 (u2 - 2) du= ʃ 2u4 - 4u2 du= [2/5u5 - 4/3u3 + C]= 2/5 (2 + x)5/2 - 4/3 (2 + x)3/2 + C
SP
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