Given that:
we should find the indefinite integral of integral -2x^-10 -2 dx using C as contstant of integration
so,
integral of (-2x^a - 2) = -2/(a+1)x^(a+1) - 2x + C
Where a is the exponent of x
we have our exponent of x as -10 from the question
so,
integral of -2x^-10 - 2
= -2/(-10+1)x^(-10+1) - 2x + C
= 2/9x^(9) - 2x + C
= (2/9x)^-9 - 2x + C