Find the anti-derivative of the integral
[(7t^2+6t-15)/t^4]dt
just divide each term by t^4 and you have
7/t^2 + 6/t^3 - 15/t^4
If that doesn't look familiar, think of it as
7t^-2 + 6t^-3 - 15t^-4
and then just apply the power rule as normal.