Evaluate : ∫(ex + 1)2 ex dx

1.	Evaluate : ∫(ex + 1)2 ex dx
Answer» Let I = ∫(e^x+ 1)² e^x dx Let e^x +1= t = e^x dx = dt I = ∫ e^x + 1)² e^x dx = ∫t² dt = \(\frac{t^3}{3}\) Now, Substitute the value of t. Hence, I = \(\frac{(e^x+1)^3}{3}\) + C

Answer»

Let I = ∫(e^x+ 1)² e^x dx

Let e^x +1= t = e^x dx = dt

I = ∫ e^x + 1)² e^x dx

= ∫t² dt

= \(\frac{t^3}{3}\)

Now,

Substitute the value of t.

Hence,

I = \(\frac{(e^x+1)^3}{3}\) + C

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