 Hello and welcome to the session. My name is Asha and I am going to help you with the following question that says, Integrate the following functions, third one is 1 upon root over 2 minus x whole square plus 1. So first let us learn a simple integral formula with the help of edge which will integrate the given function. So if we have a function not to form 1 upon root over x square plus a square then its integral with respect to x is equal to log mod x plus root over x square plus a square plus c where c is a constant. So with the help of this formula we shall integrate the given function. So this is our key idea. Let us now start with the function. The given function is 1 upon root over 2 minus x whole square plus 1. How we have to integrate this function? Therefore we have integral dx upon root over 2 minus x whole square plus 1. So let us put 2 minus x is equal to t. Now differentiating both sides with respect to x we have 0 minus 1 is equal to dt upon dx or if further we have dx is equal to dt with a negative sign. Thus the integral can further be written as integral minus dt upon root over t square plus 1 or this is further equal to taking minus sign outside the integral we have integral dt upon root over t square plus 1. Now find the formula for key idea we have minus log mod of t plus root over t square plus 1 plus c and this is further equal to minus log t 2 minus x plus root over 2 minus x whole square plus 1 plus c. Now since log x raise to the power minus 1 is equal to minus log x therefore this expression can further be written as log plus root over x whole square plus 1 raise to the power minus 1 plus c or this can further be written as log 1 upon plus root over x whole square plus 1 plus c. Now let us simplify this bracket we have 2 minus x whole square plus 1 so this is equal to 4 minus 4x plus x square plus 1 or x square minus 4x plus 5. Thus now this expression can further be written as log mod 1 upon 2 minus x plus root over x whole square minus 4x plus 5 plus c. Thus on integrating the given function we get log mod 1 upon 2 minus x plus root over x whole square minus 4x plus 5 plus c. So this completes this edition by intake kill.