For the following two (02) items: Let u = e^x x , dx and v = e^x x , dx . What is u + v equal to?

Step-by-step solution

Given u = e^x x , dx and v = e^x x , dx Adding u and v : u + v = e^x ( x + x) , dx Using the standard integral e^x (f(x) + f'(x)) , dx = e^x f(x) , where f(x) = x and f'(x) = x : u + v = e^x x From the given expression for v , differentiating with respect to x : dv dx = d dx ( e^x x , dx ) = e^x x Therefore, u + v = dv dx Answer: dv dx