Question

Integral of (dt/[sqrt(t)+25tsqrt(t)]}

From 1/75 to 3/25

I'm at a complete loss at what to do.

Answer 1

let y = t^(1/2)

dy = (1/2) t^-(1/2) dt
dt = 2 t^(1/2) dy = 2 y dy
sqrt t = y
25 t sqrt t = 25 y^3
so
integral 2 y dy/(y+25 y^3)
or
integral of 2 dy/(1 + 25 y^2)