Question

5 1
Evaluate:
S
2^x+5/x-1/x^1/3
dx​

Answer 1

Answer:

Step-by-step explanation:

Let I=∫  

(x+1)  

3

 

(x−1)e  

x

 

​

dx

⇒I=∫{  

(x+1)  

3

 

x+1−2

​

}e  

x

dx

=∫{  

(x+1)  

2

 

1

​

−  

(x+1)  

3

 

2

​

}e  

x

dx

=∫e  

x

⋅  

(x+1)  

2

 

1

​

dx−2∫e  

x

 

(x+1)  

3

 

1

​

dx

Applying integrating by parts, we get

=(  

(x+1)  

2

 

1

​

e  

x

−∫e  

x

 

(x+1)  

3

 

(−2)

​

dx)−2∫e  

x

 

(x+1)  

3

 

1

​

dx

=  

(x+1)  

2

 

e  

x

 

​

+C

Note We can use the formula

∫e  

x

[f(x)+f  

′

(x)]dx=e  

x

f(x)+C