\int_0^t(1+nu)^{-2+l/n}\,du=\int_0^t\frac{x^{-2+l/n}}{n}\,dx=\frac 1{n(-1+l/n)}\left.x^{-1+l/n}\right|_0^t=\frac{t^{l/n-1}}{l-n}