Integral Formulas

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.

List of Integral Formulas

The list of basic integral formulas is given below:

These integral formulas are equally important as differentiation formulas. Some other important integration formulas are:

Classification of Integral Formulas

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

Integral Formulas for Different Functions

Let’s learn all the integration formulas for different functions now.

Rational functions

Below are the integration formulas for rational functions.

• ∫ 1 dx = x + C

• ∫ a dx = ax+ C

• ∫ (1/x) dx = ln |x| + C

Irrational functions

Let’s see the integration formulas for irrational functions.

Trigonometric 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

Inverse trigonometric functions

Go through the integration formulas for inverse trigonometric functions here.

Hyperbolic functions

Below is the list of integration formulas for hyperbolic functions in maths.

Exponential functions

• ∫ xn dx = ((xn+1)/(n+1))+C ; n≠1

• ∫ ex dx = ex + C

• ∫ ax dx = (ax/ln a) + C ; a > 0,  a≠1

Logarithmic functions