Shri Laxmi Nidhi Institute of Mathematics where math comes alive

1. Integration as anti-derivatives (reverse of differentiation)2. Integration by substitution

3. Integration by parts (ILATE Rule)

STANDARD METHODS OF INTEGRATION AND SPECIAL INTEGRALS

Take the first function to be the function, which comes first in the word ‘ILATE’ whereI stands for the inverse t-functions like etc.L stands for the logarithmic functionA stands for the algebric function (like polynomials) T stands for the t-functionsE stands for the exponential functions

4. Integration of algebric functionsA. Rational algebric functions

Integration of forms

Integration using partial fraction

Integration of forms

Integration of form

B. Irrational algebric functions

Forms , , ,

Forms , , ,

5. Integration of trigonometric functions

Forms

Forms , , ,

Forms

Form

Form

Form

Form

When the integrand is a rational function and degree of the numerator is degree of the denominator

Perform long division

Multiple Angle Method: If the square or cube or fourth power of a sine or cosine occurs in the integrand, it is generally useful to express the square (or cube or fourth power) of sine or cosine in a series of sines or cosines of multiple angles (by using the 2A or 3A formulas of trigonometry)

“A,B” Formulae Method: If the product of a sine and cosine or of two or more sines or of two or more cosines occurs in the integrand, it is generally useful to apply the “A,B” formulae of trigonometry and express the product in a series of sines or cosines of multiple angles.