calculus
posted by melissa .
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Use C for the constant of integration.)
1/x{(x1)^1/2} dx

let
u^2 = x1
x = 1+u^2
2u du = dx
Now your integrand is
1/(1+u^2) * u * 2u du
= 2u^2/(1+u^2) du
= 2(1  1/(1+u^2)) du
That integrates to
2(u  arctan(u))+C
= 2(√(x1)  arctan√(x1))+C
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