Integral Formulas

Integral Formulas – Integration can be considered as the reverse process of differentiation or can be called Inverse Differentiation. Integration is the process of finding a function with its derivative. Basic integration formulas on different functions are mentioned here. Apart from the formulas for integration, classification of integral formulas and a few sample questions are also given here, which you can practice based on the integration formulas mentioned in this article. When we speak about integration by parts, it is with regard to integrating the product of two functions, say y = uv. Some more concepts related to integral calculus are given, so keep learning integral formulas to solve problems accurately. Also, watch the video given below to clear your concept.

List of Integral Formulas

The list of integral formulas are

    • ∫ 1 dx = x + C
    • ∫ a dx = ax+ C
    • ∫ xdx = ((xn+1)/(n+1))+C ; n≠1
    • ∫ sin x dx = – cos x + C
    • ∫ cos x dx = sin x + C
    • ∫ secdx = tan x + C
    • ∫ cscdx = -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
    • ∫ edx = ex+ C
    • ∫ adx = (ax/ln a) + C ; a>0,  a≠1

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

Integral Formulas

Classification of Integral Formulas

The above listed integral formulas are classified based on following funtions,

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

Solve Using Integral Formulas

1. Calculate ∫ 5x4 dx

2. Find \(\int x\sqrt{1+2x}\;dx\)

3. Solve\(\int \frac{1}{x^{2}+6x+25}\,dx\)

Leave a Comment

Your email address will not be published. Required fields are marked *