Integration Formulas

Integration is one of the basic operations of Calculus which serves as a tool to solve various mathematical problems. Integral calculus also helps in solving problems of physics that involve arbitrary shapes, length of a curve volume of a cube, etc. We have listed the list of integration formulas to make it easy for you. Integration is thought of as the inverse process of differentiation, which is another major branch of Calculus. Integral calculus is induced by the problem of defining and calculating the area of the section bounded by the Full List graph of functions. Integration is also referred to as finding a function when its derivative is given.

We know, Integration is introduced in the higher classes i.e. Class XI & XII. It is one of the most important topics in class XII Mathematics. There is a whole bunch of formulae students needs to know and remember to solve problems related to integral calculus.

Check out Integration Formulas notation:

The symbol for Integral is a long, styled, and slim ‘S’. After the integral symbol, we put the integrand f(x) i.e. the function we want to find the integral of. The function is symbolized with a small letter-styled version of ‘f’. dx differential of variable the x is added after the integrand, it indicates that the variable of integration is x.

Integration formula notation

Integration formulas notation

List of Integration Formulas:

The list of Integral Formulas are given below:

  • ∫ 1 dx = x + C
  • ∫ a dx = ax+ C
  • ∫ xn dx = ((xn+1)/(n+1))+C ; n≠1
  • ∫ sin x dx = – cos x + C
  • ∫ cos x dx = sin x + C
  • ∫ sec2 dx = tan x + C
  • ∫ csc2 dx = -cot x + C
  • ∫ sec x (tan x) dx = sec x + C
  • ∫ csc x ( cot x) dx = – csc x + C
  • ∫ (1/x) dx = ln |x| + C
  • ∫ ex dx = ex+ C
  • ∫ ax dx = (ax/ln a) + C ; a>0,  a≠1

Some other Integration Formulas are:

Classification of Integral Formulas

The above listed integral formulas are classified based on the following functions:

  • Rational functions
  • Irrational functions
  • Trigonometric functions
  • Inverse trigonometric functions
  • Hyperbolic functions
  • Inverse hyperbolic functions
  • Exponential functions
  • Logarithmic functions
  • Gaussian function

Solve Using Integral Formulas

1. Calculate ∫ 5x4 dx

2. Find ∫x1+2x−−−−−√dx

3. Solve∫1×2+6x+25dx

Some helpful and basic Integration Formulas

With the help of fundamental theorems of integrals, there are general results obtained those are recognized as integration formulas in indefinite integration. Such as:-

  • ∫ xn.dx = x(n + 1)/(n + 1)+ C
  • ∫ 1.dx = x + C
  • ∫ ex.dx = ex + C
  • ∫1/x.dx = log|x| + C
  • ∫ ax.dx = ax /loga+ C
  • ∫ ex[f(x) + f'(x)].dx = ex.f(x) + C

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