Can someone help me prove this? thank you!

Black and Scholes solved their now-famous PDE V/t + 1/2sigma^2 S^2^2V/S^2 + rS V/S - V = 0 with the right boundary conditions to get a solution for the value of the European Call option. this value is given by the formula C(S, t) = N(d_1)S - N(d_2)Ke^-r(T-t) d_1 = 1/sigmaSquarerootT- t[In(s/K)+(r+sigma^2/2) (T - t)d_2 = d_1 - sigmaSquarerootT-t I used the notation V instead of C, and T instead of T-t. N is the cumulative distribution function of the standard normal distribution N(x)= 1/Squareroot2pi integral_-infinity^x e^t^2/2 dt this This formula turns out to be equivalent to our expected payoff formula: V: = e^-r.T. integral_V^infinity (S - k)middot pdf(s)dS