Need help with intergration of Parts

Question

valuate the integral.

6rer/7 dr

Answer 1

u = 6r, du = 6dr; dv = e^r/7dr, so v = ∫e^r/7dr = 7e^r/7; then ∫6re^r/7dr = 6r·7e^r/7 - ∫7e^r/76dr = 42re^r/7 - 294e^r/7 + C

Answer 2

Let u = 6r and dv = e^r/7dr. Then du = 6dr and v = 7e^r/7. Then, we have:

∫ 6re^r/7dr = 42re^r/7 - 42 ∫ e^r/7dr = 42(re^r/7 - 7e^r/7) + C = 42e^r/7(r - 7) + C