Since integration is the inverse of differentiation, you can think of integration as “dividing” by d.

J. P. Ballantine [1] shows that you can formally divide by d and get the correct integral. For example, he arrives at

using long division!

[1] J. P. Ballantine. Integration by Long Division. The American Mathematical Monthly, Vol. 58, No. 2 (Feb., 1951), pp. 104-105