Basic rules of integration, important rules of integration

Also known as anti derivative

1. Integration Group 2

2. What is Indefinite Integrals? Also known as Antiderivatives A function that practices the antiderivative of another function R epresents a family of functions whose derivatives are f. An integral which is not having any upper and lower limit is known as an indefinite integral. I f F(x) is any anti-derivative of f(x) then the most general antiderivative of f(x) is called an indefinite integral and denoted, ∫f(x) dx = F(x) + C.

3. Terminologies The symbol  , also called the integral sign, denotes the operation of antidifferentiation. The function f is called the integrand. If F is an antiderivative of f, we write  f(x) dx = F(x) + C. The symbols  and dx go hand-in-hand and dx helps us identify the variable of integration. The expression F(x)+C is called the general antiderivative of f. Meanwhile, each antiderivative of f is called a particular antiderivative of f.

4. Basic Rules of Integration Rule Formula Integration of Constant Integration of constant function say ‘a’ will result in: Integration of Variable If x is any variable then; Integration of Square If the given function is a square term, then; Integration of Reciprocal  If 1/x is a reciprocal function of x, then the integration of this function is: Integration of Exponential Function The different rules for integration of exponential functions are: Rule Formula Integration of Constant Integration of constant function say ‘a’ will result in: Integration of Variable If x is any variable then; Integration of Square If the given function is a square term, then; Integration of Reciprocal  If 1/x is a reciprocal function of x, then the integration of this function is: Integration of Exponential Function The different rules for integration of exponential functions are:

5. Basic Rules of Integration Rule Formula Integration of Trigonometric Function Rule Formula Integration of Trigonometric Function

6. Important Rules of Integration Rule Formula Power Rule of Integration As per the power rule of integration, if we integrate x raised to the power n, then; Sum Rule of Integration The sum rule explains the integration of sum of two functions is equal to the sum of integral of each function. Difference Rule of Integration The difference rule of integration is similar to the sum rule. Multiplication by Constant If a function is multiplied by a constant then the integration of such function is given by: Rule Formula Power Rule of Integration As per the power rule of integration, if we integrate x raised to the power n, then; Sum Rule of Integration The sum rule explains the integration of sum of two functions is equal to the sum of integral of each function. Difference Rule of Integration The difference rule of integration is similar to the sum rule. Multiplication by Constant If a function is multiplied by a constant then the integration of such function is given by:

7. Important Rules of Integration Rule Formula Integration by parts This rule is also called the product rule of integration. It is a special kind of integration method when two functions are multiplied together. The rule for  integration by parts  is: Integration by Substitution Integration by substitution is also known as “Reverse Chain Rule” or “u-substitution Method” to find an integral. The first step in this method is to write the integral in the form: Second step, we can do a substitution as follows: Final step, substitute the equivalent values in the above form: Rule Formula Integration by parts This rule is also called the product rule of integration. It is a special kind of integration method when two functions are multiplied together. The rule for  integration by parts  is: Integration by Substitution Integration by substitution is also known as “Reverse Chain Rule” or “u-substitution Method” to find an integral.

8. Techniques on Integration Substitution Powers of sine of cosine Trigonometric Substitutions Integration by Parts Rational Functions Numerical Integration Additional Exercises