∫ x^-6 dx=

∫ x-1/3 dx=

Using the power rule of integration, we have:

∫ x^-6 dx = x^-5 / (-5) + C

where C is the constant of integration.

Alternatively, we can rewrite x^-6 as (1/x)^6 and use the power rule for negative exponents:

∫ x^-6 dx = ∫ (1/x)^6 dx = (-1/5) * (1/x)^5 + C

Either way, we get:

∫ x^-6 dx = -1/5x^5 + C