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