 Hello and welcome to the session. In this session we discuss the following question that says evaluate integral x minus 4 whole into e to the power x upon x minus 2 whole cube dx. Let's move on to the solution now. We take let i be equal to the given integral x minus 4 the whole multiplied by e to the power x upon x minus 2 whole cube dx. Now this is further equal to integral. Now we can write x minus 4 as x minus 2 minus 2 this whole multiplied by e to the power x upon x minus 2 whole cube dx. This is equal to integral x minus 2 into e to the power x dx upon x minus 2 whole cube minus integral 2 into e to the power x upon x minus 2 whole cube dx. That is we get this is equal to integral e to the power x upon x minus 2 whole square dx minus integral 2 into e to the power x upon x minus 2 whole cube dx. Now we integrate this first integral by parts. Now taking e to the power x as the second function and 1 upon x minus 2 whole square as the first function we get this is equal to first function that is 1 upon x minus 2 whole square into integral of the second function that is integral of e to the power x dx minus integral of differential of the first function that is d by dx of 1 upon x minus 2 whole square into integral of the second function that is integral of e to the power x dx dx minus integral of 2 into e to the power x upon x minus 2 whole cube dx that is this term remains as it is. So we get this is further equal to e to the power x upon x minus 2 whole square minus integral of now differentiating this expression we get minus 2 upon x minus 2 whole cube into integral of e to the power x is e to the power x dx minus integral 2 into e to the power x upon x minus 2 whole cube dx or you can say this is equal to e to the power x upon x minus 2 whole square plus integral 2 into e to the power x upon x minus 2 whole cube dx minus integral 2 into e to the power x upon x minus 2 whole cube dx. Now this term cancels with this term and we are left with e to the power x upon x minus 2 whole square plus c where c is the constant of integration so we have i is equal to this thus the given integral integral x minus 4 the whole multiplied by e to the power x upon x minus 2 whole cube dx is equal to e to the power x upon x minus 2 whole square plus c this is the final answer this completes the session hope you have understood the solution of this question.