Flag Integral Calculus> The value of the integral ∫(1+x-1/x)e x+1...
question mark

The value of the integral  ∫(1+x-1/x)ex+1/x is equal to=

Shayak Jana , 6 Years ago
Grade 12th pass
anser 1 Answers
Arun

Last Activity: 6 Years ago

Dear student
 
 
we notice that : 
(x + 1/x) ' = 1 - 1/x^2 
and so : 
x (x + 1/x) ' = x (1 - 1/x^2) = x - 1/x 

so for ----> u(x) = x+ 1/x 

we have to integrate a form that can be presented like this: 
(1+x-1/x)*e^(x+1/x) = 1*e^u(x) + x u '(x) *e^u(x) can be written like this : 
(x) ' *e^u(x) + x u '(x) *e^u(x) 
which is the derivative of ------> [ x e^u(x) ] 
and therefore we see that : 

∫ (1+x-1/x)*e^(x+1/x) dx = ∫ [ (x) ' *e^u(x) + x u '(x) *e^u(x) ] dx 

= ∫ [ (x) ' *e^u(x) + x [e^u(x)] ' ] dx 

= ∫ [ x e^u(x) ] ' dx 

= x e^u(x) + C 

conclusion : 

∫ (1+x-1/x)*e^(x+1/x) dx = x e^(x+1/x) + C 
 
Regards
Arun

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...