Question

Find the value of [xe (1 + x2) dx.​

Answer 1

Step-by-step explanation:

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