integral(1+x-x^-1)e^x+x^-1dx=? solution please….......................
integral(1+x-x^-1)e^x+x^-1dx=? solution please….......................
Pavani , 5 Years ago
Grade 12
Integral Calculus> integral (1+x-x^-1)e^x+x^-1 dx=? solution...
1 AnswersArun
Last Activity: 5 Years ago
e same way as for : ∫ Lnx dx = x*Lnx - x
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
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
Provide a better Answer & Earn Cool Goodies
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Other Related Questions on integral calculus
The area of a square field is 640000cm2.what is its area in hectares
The area of a square field is 640000cm2.what is its area in hectares
integral calculus
1 Answer Available
Last Activity: 2 Years ago
Please solve this integration. I am facing difficulty in it How to solve this. Please solve anyone. Humble request
Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request
integral calculus
0 Answer Available
Last Activity: 2 Years ago
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
integral calculus
0 Answer Available
Last Activity: 2 Years ago
how to solve this?
this is interger type question .
how to solve this?
this is interger type question .
this is interger type question .
integral calculus
0 Answer Available
Last Activity: 3 Years ago