Question

integration of xe^x/(x+1)^2 dx​

Answer 1

Answer:

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