An acronym that is very helpful to remember when using integration by parts is LIATE. Whichever function comes first in the following list should be u: L Logatithmic functions ln(x), log2(x), etc. Following the LIATE rule, **u = x and dv = sin(x)dx** since x is an algebraic function and sin(x) is a trigonometric function.

Contents

- 1 What is the Liate rule?
- 2 What is the formula of product rule of integration?
- 3 What is the integration rule?
- 4 How do you use Liate?
- 5 What is integration of LNX?
- 6 What is U and V in integration by parts?
- 7 What is the rule for integration by parts?
- 8 What is the substitution rule of integration?
- 9 Does chain rule apply to integration?
- 10 When can you use u-substitution?

## What is the Liate rule?

For those not familiar, LIATE is a guide to help you decide which term to differentiate and which term to integrate. L = Log, I = Inverse Trig, A = Algebraic, T = Trigonometric, E = Exponential. The term closer to E is the term usually integrated and the term closer to L is the term that is usually differentiated.

## What is the formula of product rule of integration?

The integration of uv formula is a special rule of integration by parts. Here we integrate the product of two functions. If u(x) and v(x) are the two functions and are of the form ∫u dv, then the Integration of uv formula is given as: ∫ uv dx = u ∫ v dx – ∫ (u’ ∫ v dx) dx. ∫ u dv = uv – ∫ v du.

## What is the integration rule?

This rule is essentially the inverse of the power rule used in differentiation, and gives us the indefinite integral of a variable raised to some power. Just to refresh your memory, the integration power rule formula is as follows: ∫ ax ^{n} dx = a. x ^{n}^{+}^{1}.

## How do you use Liate?

Following the LIATE rule, u = x and dv = sin(x)dx since x is an algebraic function and sin(x) is a trigonometric function. = -x cos(x) + sin(x) + C. WARNING: This technique is not perfect! There are exceptions to LIATE.

## What is integration of LNX?

Answer: The final integral of ln x is x ln(x) − x + C. Go through the explanation to understand better. Explanation: To solve ∫ln(x)dx, we will use integration by parts: ∫u dv=uv − ∫vdu. Let u = ln(x) and dv = dx ⇒ v = x.

## What is U and V in integration by parts?

u is the function u(x) v is the function v(x) u’ is the derivative of the function u(x)

## What is the rule for integration by parts?

In the integration by parts, the formula is split into two parts and we can observe the derivative of the first function f(x) in the second part, and the integral of the second function g(x) in both the parts. For simplicity, these functions are often represented as ‘u’ and ‘v’ respectively. The. ∫ u dv = uv – ∫ v du.

## What is the substitution rule of integration?

The substitution rule is a trick for evaluating integrals. It is based on the following identity between differentials (where u is a function of x): du = u dx. Most of the time the only problem in using this method of integra- tion is finding the right substitution. Example: Find ∫ cos 2x dx.

## Does chain rule apply to integration?

Since integration is the inverse of differentiation, many differentiation rules lead to corresponding integration rules. Consider, for example, the chain rule. The formula forms the basis for a method of integration called the substitution method.

## When can you use u-substitution?

U-Substitution is a technique we use when the integrand is a composite function. What’s a composite function again? Well, the composition of functions is applying one function to the results of another.