How do you integrate $(x + 2)^2 / x^(1/3)$ ?

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Answer 1 · 2016-10-14T19:57:55

Expand and integrate term by term.

$(x+2)^2/x^(1/3) = (x^2+4x+4)/x^(1/3)$

$= x^2/x^(1/3)+(4x)/x^(1/3)+4/x^(1/3)$

$= x^(5/3)+4x^(2/3)+4x^(-1/3)$

$int (x+2)^2/x^(1/3) dx = int (x^(5/3)+4x^(2/3)+4x^(-1/3)) dx$

$= 3/8x^(8/3)+ 4* 3/5 x^(5/3) +4 (3/2)x^(2/3) +C$

Simplify as desired.

How do you integrate (x + 2)^2 / x^(1/3) (x + 2)^2 / x^(1/3)?