 Hi and welcome to our session. Let us discuss the following question. The question says, evaluate integral of x into e to the power x divided by 1 plus x whole square with respect to x. Again with the solution, let i is equal to integral of x into e to the power x divided by 1 plus x whole square with respect to x. However, we will first add and subtract 1 in the numerator. So this is equal to integral x plus 1 minus 1 into e to the power x divided by 1 plus x whole square dx. Now this is equal to integral 1 by 1 plus x into e to the power x dx minus integral 1 by 1 plus x whole square into e to the power x dx. Now consider integral 1 by 1 plus x into e to the power x dx. Now we will integrate this function by using i-late rule. So treating 1 by 1 plus x as the first function and e to the power x as second function, we get 1 by 1 plus x into integral e to the power x dx minus integral derivative of 1 by 1 plus x into integral e to the power x dx. Now this is equal to 1 by 1 plus x into e to the power x minus derivative of 1 by 1 plus x is minus 1 by 1 plus x whole square into e to the power x dx. This is equal to e to the power x divided by 1 plus x plus integral e to the power x divided by 1 plus x whole square dx. i is equal to e to the power x by 1 plus x plus integral e to the power x divided by 1 plus x whole square dx minus integral e to the power x divided by 1 plus x whole square dx. And this is equal to e to the power x divided by 1 plus x. Hence our required answer is e to the power x divided by 1 plus x. So this completes the session by and take care.