F(x)=5(x-5)e^(0,2x-1)+5x Montrer que F est une primitive de f f(x)=5+xe^(0,2x-1)

f(x) = u(x)v(x) <=> f'(x) = u'v + uv'

F'(x) = 5(1e^[0,2x-1] + 0,2(e^[0,2x-1])(x-5)) +5
= 5 + 5(e^(0,2x-1)(1+x/5-1)
= 5 + e^(0,2x-1)
= f(x)

Tada.