Integral Calculus and Differential Equations | Mathematics for NDA PDF Download

List of Integral Formulas

The list of basic integral formulas is given below:

• ∫ 1 dx = x + C

• ∫ a dx = ax+ C

• ∫ x_n dx = ((x_n+1)/(n+1))+C ; n≠1

• ∫ sin x dx = – cos x + C

• ∫ cos x dx = sin x + C

• ∫ sec 2x dx = tan x + C

• ∫ csc 2x 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

• ∫ e_x dx = e_x + C

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

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

• ∫ sec 2x dx = tan x + C

• ∫ csc 2x 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

Logarithmic functions

Integral Formulas for Some Special Functions

As we have already gone through integral formulas for exponential functions, logarithmic functions, trigonometric functions and some basic functions. Let’s have a look at the additional integration formulas, i.e. the integral formulas for some special functions listed below