Integration by Parts This method is used to integrate the product of two functions. If f( x) and g( x) be two integrable functions, then
( i) We use the following preferential order for taking the first function. Inverse→ Logarithm→ Algebraic → Trigonometric→ Exponential. In short we write it HATE.
( ii) If one of the function is not directly integrable, then we take it a the first function.
( iii) If only one function is there, i. e., ∫log x dx, then 1( unity) is taken as second function.
( iv) If both the functions are directly integrable, then the first function is chosen in such a way that its derivative vanishes easily or the function obtained in integral sign is easily integrable.
Integral of the Form