maths maths maths maths

Question

math maths maths maths maths maths maths maths maths maths maths amths

Answer 1

xe^x and e^x x are the same thing

I wonder if the question relates to how you set up integration by parts

integration by parts: ∫v du = uv - ∫u dv

v = x, dv = 1

du = e^x , u = e^x

∫ = e^x x - e^x = e^x (x - 1) + C

Do it the other way:

v = e^x, dv = e^x

du = x, u = x²/2

∫ = e^x *x - e^x*x³/6 This is (obviously?) not going to work. (Look up the rule for choosing v and du when integrating by parts)