Dr. Brajesh Kumar Jha

  Integration by Part If u and v are two functions of x, then Remark: The proper choice of u and v is very important to apply integration by part. We can choose the first function (u) as the function which comes first in the word ILATE. Here I stands for the inverse trigonometric function (Ex. ) L stands for logarithmic function (Ex. ) A stands for the algebraic functions (Ex. ,   etc.) T stands for the trigonometric functions (Ex. ) E stands for the exponential functions. (Ex. ) Example 1: Evaluate Solution: Here as per the above remark ILATE   (Algebraic function) comes first and   (trigonometric function). Thus let   and . Now by formula Example 2: Evaluate   Solution: Here as per the above remark ILATE   (Algebraic function) comes first and   (trigonometric function). Thus let   and . Now by formula Where   and Here in second part of integration ( ) we will apply in...