I want to compute the posterior predictive distribution p(x~x1,...,x100)

Given that I already found the posterior distribution follows Gamma(52,1+21i=1100(xi75)2) and x1,...,x100 follows N(75,1) .

I know to compute for the posterior predictive distribution we have to calculate p(x~x)=0p(x~)p(x)d that is integral of the product of posterior distribution (gamma given above) and the distribution of the new data ( normal distribution N(75.1) ).

Thank you!