Question

26. Jxe/(x+1)2 dx is equal to (a) ex/(x + 1) + k (b) ex/x+k (c) e + k​

Answer 1

Answer:

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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