NDA Mathematics Question (2025) — Solution

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