The integral of 1+3x
So, when you integrate you 'add one to the power and then divide by the new power' (don't worry, i know this probably doesn't sound like it makes much sense)
Take an example, The integral of x^n = (x^(n+1))/(n+1) + C , (Or, in words, the integral of x to the power of n equals x to the power of n plus one all divided by n plus one plus C) , where 'n' is any number and C is a constant (i.e. a number that we don't know).
So, for your equation 1 + 3x you can say that:
1 + 3x = 1x^0 + 3x^1
So when you integrate this it becomes:
(1x^1)/1 + (3x^2)/2 + C = x + (3/2)x^2 + C