What is the denominator of this fraction?

I am learning how to use the present participle in English.

He won the Nobel Prize for that thesis.

We should learn about ancient civilizations.

Considering his social status, he received special treatment.

I want to halve the amount of this recipe.

The calculation of an indefinite integral can be considered as the reverse operation of differentiation.

The calculation of definite integrals is an important part of calculus.

Variational method is a branch of mathematics used to find the minimum and maximum values of functions.

In order to calculate the integral constant, it is necessary to solve the differential equation.