ILATE Rule for Single Function
For a single function, ILATE Rule is still applicable. Identify the nature of the function and follow the sequence: Inverse, Logarithmic, Algebraic, Trigonometric, and Exponential.
When dealing with a single function, apply the ILATE rule by prioritizing functions in the order of Inverse, Logarithmic, Algebraic, Trigonometric, and Exponential.
Example: ∫ln(x) dx.
Solution:
∫1.ln(x) dx
In this case, ln(x) is a logarithmic function and 1 is algebraic function
According to ILATE, logarithmic functions take precedence over algebraic functions. So,
- First Function: ln(x)
- Second Function: 1
∫ 1.ln x dx
= (ln x) ∫ 1 dx – ∫ [d/dx (ln x) ∫ 1 dx] dx
= (ln x) x – ∫ (1/x) (x) dx
= x ln x – ∫ 1 dx
= x ln x – x + C
= x(ln x – 1) + C
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ILATE Rule
ILATE rule stands for Inverse Trigonometric Function, Logarithmic Function, Algebraic Function, Trigonometric Function, and Exponential Function. It tells about the priority order in which functions are selected for their integration. It is an important concept in solving integration problems.
This formula is also called the ‘uv integration formula’. If we have to find the integration of a function that is a product of two functions then we use the ILATE rule of integration. In this article, we will learn about, What the is ILATE Rule, How to Apply the ILATE Rule, ILATE Rule Examples, and others in detail.
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