Question

Evaluate ∫ (x+1)2 ex dx

Answer 1

∫ (x+1)2 ex dx

y = ∫(x2 + 2x + 1) ex dx

y = ∫(x2 + 2x)ex dx + ∫ex dx

We know that,

∫(f(x) +f’(x))ex dx = f(x) ex

Here,

f(x) = x2

Then,

f’(x) = 2x

y = x2ex + ex + c

y = (x2 + 1)ex + c