How do you integrate fractions?
Mia Phillips
Updated on February 25, 2026
If you are asked to integrate a fraction, try multiplying or dividing the top and bottom of the fraction by a number. Sometimes it will help if you split a fraction up before attempting to integrate. This can be done using the method of partial fractions.
What are the rules of antiderivative?
To find antiderivatives of basic functions, the following rules can be used:
- xndx = xn+1 + c as long as n does not equal -1. This is essentially the power rule for derivatives in reverse.
- cf (x)dx = c f (x)dx.
- (f (x) + g(x))dx = f (x)dx + g(x)dx.
- sin(x)dx = – cos(x) + c.
How do you solve the integral of a quadratic equation in the denominator?
INTEGRATE QUADRATIC FUNCTION IN DENOMINATOR. We have to express ax2+bx+c as sum or difference of two square terms to get the integrand in one of the standard forms.
What is the antiderivative calculator?
Antiderivative Calculator is a free online tool that displays the antiderivative (integration) of a given function. BYJU’S online antiderivative calculator tool makes the calculation faster, and it displays the integrated value in a fraction of seconds.
What is the antiderivative formula?
An antiderivative of a function f(x) is a function whose derivative is equal to f(x). That is, if F′(x)=f(x), then F(x) is an antiderivative of f(x)….Exercise 6.
| Function | General antiderivative | Comment |
|---|---|---|
| (ax+b)n | 1a(n+1)(ax+b)n+1+c | for a,b,c,n any real constants with a≠0, n≠−1 |
What is the formula for the antiderivatives of powers of X?
Formula for the antiderivatives of powers of x. The general antiderivative of f(x) = x n is. where c is an arbitrary constant. Example: Find the most general derivative of the function f(x) = x –3.
What is the definition of antiderivative in math?
Definition of Antiderivative. A function F is called an antiderivative of f on an interval I if F’(x) = f(x) for all x in I. The general antiderivative of f(x) = x n is. where c is an arbitrary constant.
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.
How do you check if an antiderivative is correct?
Since the derivative of the wanted antiderivative is the given function, checking for correctness is easy. 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.
