Question

E
(1) Integrate the following w.r. to x
хех
(a)
(b) ex
(x + 1)2​

Answer 1

Step-by-step explanation:

x+1

e

x

+C

Let I=∫

(1+x)

2

xe

x

dx

I=∫

(1+x)

2

(x+1−1)e

x

dx

I=∫

(1+x)

e

x

dx−∫

(1+x)

2

e

x

dx

Applying integration by parts in first integral, we get

I=

(1+x)

e

x

−∫−(

(1+x)

2

1

)e

x

dx−∫

(1+x)

2

e

x

dx+C

I=

(1+x)

e

x

+∫(

(1+x)

2

1

)e

x

dx−∫

(1+x)

2

e

x

dx+C

I=

(1+x)

e

x

+C