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

int(x^(1/2)+2x^(1/2)+x^(3/2))dx =

int(x^(1/3)+2x^(1/2)+x^(3/2))dx

int((1-x^(-2))/(x^(1/2)-x^(-1/2))-(2)/(x^(3/2))+(x^(-2)-x)/(x^(1/2)-x^(-1/2)))dx

Show that int_(1)^(2)(x+(1)/(x))^(3//2)((x^(2)-1)/(x^(2)))dx = ((5)/(2))^(3//2) - (8sqrt(2))/(5)

Find dy/dx x^(1/2) y^(-1/2) + x^(3/2) y^(-3/2) = 0

int((1-x^(- 2))/(x^(1//2)-x^(-1//2))-2/(x^(3//2))+(x^(- 2)-x)/(x^(1//2)-x^(-1//2)))dx

int(x^((1)/(3))+2x^((1)/(2))+x^((3)/(2)))dx

Evaluate: int_(0)^(1//2) (sin^(-1)x)/((1-x^(2))^(3//2)) dx

If the value of the integral int_(0)^(1//2) (x^(2))/((1-x^(2))^(3//2)) dx is (k)/(6) then k is equal to :

Simpify : (1)/((4x^3-3x)^2)-{((3sqrt(1-x^2))/(x)-((1-x^2)^(3/2))/(x^3))/(1-3((1-x^2)/(x^2)))}^2 .