Can someone help me with this question:
Find a continuous function f and a number a such that:
$\displaystyle 1 + \int_{a}^x \frac{f(t)}{t^5}\ dt = 4x^{-1} \qquad {\color{red}\star}$
Differentiate both sides (the left hand side of course using one of the Fundamental Theorems of Calculus) to get: $\displaystyle \frac{f(x)}{x^5} = -4x^{-2}$
Solve for $\displaystyle f(x)$.
Now go back to $\displaystyle {\color{red}\star}$ and substitute in $\displaystyle f(t)$ now that we know what $\displaystyle f$ is.