 Hello and welcome to the session I am Deepika here. Let's discuss a question which says integrate the following function x into e raise to power x upon 1 plus x whole square. Let us first understand the integral of the type e raise to power x fx plus f dash x equal to 2 power x into fx plus this is the key idea behind that question. We will take the help of this key idea to solve the above question. So let's start the solution. Now we have to integrate x into e raise to power x upon 1 plus x whole square. Now according to our key idea we will express the integral as the sum of two integrals one consisting of fx containing f dash x. So our given integral can be written as e raise to power x over 1 plus x whole square is equal to integral of e raise to power x 1 upon 1 plus x whole square n equal to 1 plus x whole square minus 1 over 1 plus x whole square n equal to integral of e raise to power x 1 over 1 plus x 1 over 1 plus x whole square. Note that the derivative of 1 over 1 plus x is minus 1 over minus 1 over 1 plus x whole square. The given integral therefore e raise to power x upon 1 plus x whole square is e raise to power x 1 plus x. Take care.