## What does I stand for in Ilate?

ILATE stands for: I: Inverse trigonometric functions : arctan x, arcsec x, arcsin x etc. L: Logarithmic functions : ln x, log5(x), etc. A: Algebraic functions. T: Trigonometric functions, such as sin x, cos x, tan x etc.

## What is the formula for Ilate?

ILATE rule is a rule that is most commonly used in the process of integration by parts and it makes the process of selecting the first function and the second function very easy. The integration by parts formula can be written in two ways: ∫ u dv = uv – ∫ v du.

**What is the Ilate rule?**

In integration by parts, we have learned when the product of two functions are given to us then we apply the required formula. The integral of the two functions are taken, by considering the left term as first function and second term as the second function. This method is called Ilate rule.

**How do you use Liate rule?**

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.

### What is the integration of Xsinx?

The formula for the integral of x sin x is given by, ∫xsinx dx = −x cos x + sin x + C, where C is the integration constant. We can evaluate this integral using the product rule of integration where x is the first function and sin x is the second function and x sin x is written as the product of these two functions.

### What is by parts rule?

In Integration by Parts, we have learned when the product of two functions is given to us then we apply the required formula. The integral of the two functions is taken, by considering the left term as the first function and the second term as the second function. This method is called the Ilate rule.

**What is Liate algebra?**

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 correct Liate or Ilate?**

Originally Answered: Which is correct, LIATE or ILATE? ILATE is the correct one.

#### What is integration of cos2x?

Solution. The integral of cos(2x) is (1/2)sin(2x) + C, where C is a constant.

#### How is chain rule derived from integration by parts?

After the first integration by parts, the integral we come up with is ∫xexdx, which we had dealt with in the first example. We took u=lnx and v=x. as being the derivative (via the chain rule) of ln(1+x2)….Exercises

- ∫lnxdx=?
- ∫xexdx=?
- ∫(lnx)2dx=?
- ∫xe2xdx=?
- ∫arctan3xdx=?
- ∫x3lnxdx=?
- ∫ln3xdx=?
- ∫xlnxdx=?

**What is the derivative of Xsinx?**

xcosx + Sinx

The derivative of xSinx is xcosx + Sinx.

**What is the integration of tan2x?**

The integral of tan 2x is (-1/2)ln |cos 2x| + C which can be calculated using the substitution method followed by integral of tan x formula or by expressing tan 2x in terms of sin and cos.

## What does sin2t mean?

The sin2x formula is the double angle identity used for sine function in trigonometry. Trigonometry is a branch of mathematics where we study the relationship between the angles and sides of a right-angled triangle.

## What is sin2a?

⇒ sin 2A = 2 sin A cos A. Note: In the above formula we should note that the angle on the R.H.S. is half of the angle on L.H.S. Therefore, sin 60° = 2 sin 30° cos 30°. The above formula is also known as double angle formulae for sin 2A.