$Version
(*12.2.0 for Microsoft Windows (64-bit) (December 12, 2020)*)
f[v_] := NIntegrate[
1/2 (4 ((1 - v) Exp[-2/5 t] - 1)/((1 - v) Exp[-2/5 t] + 1)^5 -
1)^2, {t, 0, 2/5 Log[99 (1 - v)]}];(*With mumerics*)
Plot[f[v], {v, 0.0098, 0.99}]
g = Integrate[
1/2 (4 ((1 - v) Exp[-2/5 t] - 1)/((1 - v) Exp[-2/5 t] + 1)^5 -
1)^2, {t, 0, 2/5 Log[99 (1 - v)]}, Assumptions -> v > 0](*Symbolic solution*)
Plot[Evaluate[g[[1]]], {v, 0.0098, 0.99}]
