Question

Evaluate x-3/x-1^3 e^x​

Answer 1

Step-by-step explanation:

Let I=∫ex{(x−1)3x−3}dx=∫ex{(x−1)2x−1−2}dx

=∫ex{(x−1)21−(x−1)32}dx

Let f(x)=(x−1)21⇒f′(x)=(x−1)3−2

Now  know that, ∫ex{f(x)+f′(x)}dx=exf(x)+C

∴I=(x−1)2ex+C