An even integer can be expressed as "2x"

Three consecutive even integers:

2x, 2(x+1) and 2(x+2)

The second such integer is 2(x+1)

Three times the second integer is 3(2(x+2))

the sum of the other two integers (1st and 3rd) is (2x+2(x+1))

3(2(x+1)) + (2x+2(x+1)) - 1

3(2x+1) + (2x+(2x+2)) - 1

6x + 3 + (4x + 2) - 1

10x + 5 - 1

since the even integer is '2x', the answer is

5(2x) + 5 - 1

or, 5(2x+1) - 1

10x + 4