lol. When you integrate the 1st term on the RHS, integral of $\displaystyle e^{kt}$ is $\displaystyle e^{kt}/k$ which cancels out the k in the numerator. The integral of the LHS is $\displaystyle ue^{kt}$ itself. The constant c is a constant of integration. First just integrate on both sides and divide both sides by$\displaystyle e^{kt}$. You will arrive at the answer. Hope this helps.