What does the ILATE Rule help with in integration?

The ILATE Rule is a mnemonic device used to help select which function to differentiate and which to integrate when applying the technique of Integration by Parts. This rule suggests a priority order for choosing functions based on the acronym itself:

• I: Inverse Trigonometric Functions (e.g., arcsin, arccos)

• L: Logarithmic Functions (e.g., ln(x))

• A: Algebraic Functions (e.g., polynomials like x²)

• T: Trigonometric Functions (e.g., sin(x), cos(x))

• E: Exponential Functions (e.g., e^x)

When faced with the task of integrating a product of functions, following the ILATE hierarchy can make the integration process more manageable. By selecting the function from this priority list as the one to differentiate (the "u" in the integration by parts formula), you are typically able to simplify the integral more efficiently.

While the other options touch on important aspects of integration, they do not directly relate to the purpose of the ILATE Rule. For instance, the concept of substitution involves a different technique in integration. Identifying limits of integration pertains to definite integrals, and estimating area under curves is more aligned with numerical methods or geometric