   Chapter 7.R, Problem 1CC

Chapter
Section
Textbook Problem

# State the rule for integration by parts. In practice, how do you use it?

To determine

To Discuss: Integration by Parts

Explanation

Calculation:

Formula: Integration by parts, uvdx=uvdxu'(vdx)dx

Here, we will be calling u as the first function and v as the second function.

While computing integrals, we use either substitution method, partial fraction method in case of rational function or integration by parts. As such there is no general method to find integration of a given function. But still we have some guiding rules to find integration of a function. While finding integral by using integration by parts, we use ILATE principle, where

I stands for inverse trigonometric function

L stands for logarithmic function

A stands for algebraic function

T stands for trigonometric function

E stands for exponential function

We chose one of them as the first function which comes first in the list ILATE. For example if the integrand is the product of logarithmic function (L) and trigonometric function(T), then chose logarithmic function as the first function and trigonometric function as the second function

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