Evaluate ∫ (x+1)2 ex dx

1.	Evaluate ∫ (x+1)2 ex dx
Answer» ∫ (x+1)² e^x dx y = ∫(x² + 2x + 1) e^x dx y = ∫(x² + 2x)e^x dx + ∫e^x dx We know that, ∫(f(x) +f’(x))e^x dx = f(x) e^x Here, f(x) = x² Then, f’(x) = 2x y = x²e^x + e^x + c y = (x² + 1)e^x + c

Answer»

∫ (x+1)² e^x dx

y = ∫(x² + 2x + 1) e^x dx

y = ∫(x² + 2x)e^x dx + ∫e^x dx

We know that,

∫(f(x) +f’(x))e^x dx = f(x) e^x

Here,

f(x) = x²

Then,

f’(x) = 2x

y = x²e^x + e^x + c

y = (x² + 1)e^x + c

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