Some Standard Formulae Using Substitution
 =
 =
 =
 = log(x + c
 =


Form  Working rule 
Divide numerator and denominator both by cos^{2} x, replace sec^{2} x, if any, in denominator by (1 + tan^{2} x) and put tan x = t. So that sec^{2} x dx = dt  
where m, n âˆˆ N


Write sin x and cos xin terms of tan(x/2) and then substitute for tan (x/2) = t  
In this integral express numerator asÎ» (denominator) + Î¼(differentiation of denominator) + Î³.
Find Î», Î¼, and Î³ by comparing coefficients of sin x, cos x and constant term and split the integral into sum of three integrals.


This linear factor (px+ q) is expressed in terms of the derivative of the quadratic factor ax^{2} +bx + c together with a constant as px + q =Î»(d/dx) {ax^{2} + bx +c} + Î¼ â‡’ px + q =Î»(2ax + b) + Î¼.
Here we find Î» and Î¼by comparing coefficients


Substitute  
Substitute 