int 1/(x^3*sqrt(x^2)) dx

Indefinite integral

integral1/(x^3 sqrt(x^2)) dx = -sqrt(x^2)/(3 x^4) + constant

Plot

Plot
Plot

Alternate form assuming x is real

-abs(x)/(3 x^4) + constant

Alternate form of the integral

-1/(3 (x^2)^(3/2)) + constant

Alternate form assuming x>0

-1/(3 x^3) + constant

Series expansion of the integral at x=0

-sqrt(x^2)/(3 x x^3) + O(x^6)
(Puiseux series)

Series expansion of the integral at x=∞

-1/(3 x^3) + O((1/x)^6)
(Laurent series)