## What is the antiderivative of a rational function?

The antiderivative of a rational function is always expressible in a closed form, which only can comprise, except a rational expression summand, summands of logarithms and arcustangents of rational functions. x2+2pjx+qj x 2 + 2 x + q j of the denominator (which have no real zeroes).

**What are the rules and antiderivatives?**

Basic Rules of Antiderivatives The antiderivative of a standalone constant is a is equal to ax. A multiplier constant, such as a in ax, is multiplied by the antiderivative as it was in the original function. For example, if f(x) = ax, F(x) = ½*a*x².

**What is anti differentiation?**

Definition of antidifferentiation mathematics. : integration sense 3 Antidifferentiation is just differentiation backwards. The derivative of sin x is cos x, so the antiderivative of cos x is sin x; the derivative of x3 is 3×2, so the antiderivative of 3×2 is x3—you just go backwards.

### What is the antiderivative of a quotient?

The integral quotient rule is the way of integrating two functions given in form of numerator and denominator. This rule is also called the Antiderivative quotient or division rule. The formula for the Integral Division rule is deduced from the Integration by Parts u/v formula.

**What is the meaning of antiderivative?**

In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F’ = f.

**What is the difference between antiderivative and integral?**

In additionally, we would say that a definite integral is a number which we could apply the second part of the Fundamental Theorem of Calculus; but an antiderivative is a function which we could apply the first part of the Fundamental Theorem of Calculus.

#### What is the anti derivative of sin?

The anti-derivative of sinx is −cosx+C and the anti-derivative of cosx is sinx+C.

**What is the anti derivative of sin2x?**

Therefore, the anti derivative of sin2x is −21cos2x. Was this answer helpful?

**Is anti differentiation the same as integration?**

The former, (Riemann) integration, is roughly defined as the limit of sum of rectangles under a curve. On the other hand, antidifferentiation is purely defined as the process of finding a function whose derivative is given.

## What is the derivative of a rational function?

Derivatives of Rational Functions. Remember a rational function is a function h(x) such that h(x) = f(x) g(x), where f(x) and g(x) are polynomial functions. The derivative of a rational function may be found using the quotient rule:

**How to find the antiderivatives of a function?**

You just take the derivative, and see if it is the given function. Also, antiderivatives of functions happen to be not just one function, but a whole family of functions. This family can be written as a polynomial plus c, where c stands for any constant. Try the free Mathway calculator and problem solver below to practice various math topics.

**What is the general antiderivative of f (x) = x n?**

The general antiderivative of f (x) = x n is where c is an arbitrary constant. The tables shows the derivatives and antiderivatives of trig functions. Scroll down the page for more examples and solutions on how to use the formulas.

### What is the opposite of a derivative?

Antiderivatives are the opposite of derivatives. An antiderivative is a function that reverses what the derivative does. One function has many antiderivatives, but they all take the form of a function plus an arbitrary constant. Antiderivatives are a key part of indefinite integrals.