Question

integrity (x-3) /(x-1) ³ ex dx​

Answer 1

Step-by-step explanation:

Let I=∫e

x

{

(x−1)

3

x−3

}dx=∫e

x

{

(x−1)

2

x−1−2

}dx

=∫e

x

{

(x−1)

2

1

−

(x−1)

3

2

}dx

Let f(x)=

(x−1)

2

1

⇒f

′

(x)=

(x−1)

3

−2

Now know that, ∫e

x

{f(x)+f

′

(x)}dx=e

x

f(x)+C

∴I=

(x−1)

2

e

x

+C