need help with an integral (1 Viewer)

[andybandy]

show that the integral of ln(x)/(1+x^2) is 0 and the limits are 2 and 1/2, substitution is u=1/x

 

[Carrotsticks]

Is this in response to this thread: http://community.boredofstudies.org/showthread.php?t=296191&p=6422376&viewfull=1#post6422376

 

[nightweaver066]

Edit: ^ lol

 

[asianese]

lol mathtype!//word

 

[nightweaver066]

ugly integral sign

 

[andybandy]

yes it is carrotsticks

 

[RealiseNothing]

yes it is carrotsticks

You're kidding right...

right?

 

[Sy123]

hahaha this thread

 

[andybandy]

is it suppose to be easy or something? im just not getting it :/

 

[mahmoudali]

hahaha this thread

why you laughing i find it extremely cute

 

[hit patel]

Can this question be done without substitution? If so please if possible show me how.

Thanks

 

[Sy123]

Can this question be done without substitution? If so please if possible show me how.

Thanks

This integral has no elementary indefinite integral, so I sincerely doubt it can be done without substitution.
Moreover the bounds 2 and 1/2 are very special and designed for the specific sub u=1/x

 

[hit patel]

This integral has no elementary indefinite integral, so I sincerely doubt it can be done without substitution.
Moreover the bounds 2 and 1/2 are very special and designed for the specific sub u=1/x

Yes it looked as so to me but just wanted to confirm.

 

[anomalousdecay]

This integral has no elementary indefinite integral, so I sincerely doubt it can be done without substitution.
Moreover the bounds 2 and 1/2 are very special and designed for the specific sub u=1/x

You can use integration by parts........

should get I = (lnx)(tan^-1(x)) - Integration of ((tan^-1(x))/x)dx

But it gets very messy.

 

[Sy123]

You can use integration by parts........

should get I = (lnx)(tan^-1(x)) - Integration of ((tan^-1(x))/x)dx

But it gets very messy.

Can you tell me how you would continue from:

?

Because I don't think that is possible with elementary functions

 

[anomalousdecay]

Can you tell me how you would continue from:

?

Because I don't think that is possible with elementary functions

1/x =dv, v=lnx.

tan^-1(x) = u

du = dx/(1 + x^2)


I = (lnx)(tan^-1(x)) - (lnx)(tan^-1(x)) + I.


Damn. I hate it when that happens. All I did was prove 0=0.

You're right, only use substitution.

 

[andybandy]

Im assuming this is extension 2 ?

 

[anomalousdecay]

Im assuming this is extension 2 ?

Yes