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.

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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.

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Exponential functions

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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