Integral formulas are basic tools in calculus that make it easier to calculate integrals, which are needed to solve problems that involve areas, volumes, and adding up numbers. Integral formulas give you a methodical way to check integrals, no matter if they are definite or undefined. They include many different methods and rules, like the Fundamental Theorem of Calculus, which connects the ideas of differentiation and integration. Other examples are partial fractions, substitution, and integration by parts. Learning these formulas not only makes hard sums easier, but it also helps us understand the basic ideas behind math better. Integral formulas are very important for both academic and practical uses because they are used a lot in physics, engineering, economics, and many other fields.
The list of basic integral formulas is given below:
These integral formulas are equally important as differentiation formulas. Some other important integration formulas are:
The integral formulas can be classified based on following functions.
Rational functions
Irrational functions
Trigonometric functions
Inverse trigonometric functions
Hyperbolic functions
Inverse hyperbolic functions
Exponential functions
Logarithmic functions
Gaussian functions
Let’s learn all the integration formulas for different functions now.
Below are the integration formulas for rational functions.
∫ 1 dx = x + C
∫ a dx = ax+ C
∫ (1/x) dx = ln |x| + C
Let’s see the integration formulas for irrational functions.
Integration formulas for trigonometric functions are listed below:
∫ sin x dx = – cos x + C
∫ cos x dx = sin x + C
∫ sec2x dx = tan x + C
∫ csc2x dx = -cot x + C
∫ sec x (tan x) dx = sec x + C
∫ csc x ( cot x) dx = – csc x + C
Go through the integration formulas for inverse trigonometric functions here.
Below is the list of integration formulas for hyperbolic functions in maths.
∫ xn dx = ((xn+1)/(n+1))+C ; n≠1
∫ ex dx = ex + C
∫ ax dx = (ax/ln a) + C ; a > 0, a≠1
An integral formula provides a method to evaluate the integral of a function, representing the area under the curve of that function or the accumulation of quantities.
Integral tables offer precomputed antiderivatives for various functions, simplifying the process of finding integrals for complex or unfamiliar functions.