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Integral of t/1+t^2

  • Thread starter rojak44
  • Start date
  • #1
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hello there,im having trouble with this question..
find int t/1+t^2 dt

my answer is 1/2 ln t (1+t^2)+c
but the answer that i have copy is 1/2 ln (1+t^2)+c
maybe i have copy it wrongly,can someone tell me which one is right?
thx.. :smile:
 

Answers and Replies

  • #2
exk
119
0
How did you get your answer?
 
  • #3
13
0
im using the integration using substitution..
im confuse right now.. can anyone give me the full calculation or what method i should use.
 
  • #4
rock.freak667
Homework Helper
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31
[tex]\frac{t}{1+t^2} dt[/tex]

Let [itex] u=1+t^2[/itex] what is [itex]\frac{du}{dt}[/itex]? then what is dt in terms of du?
 
  • #5
13
0
here it is,pls correct me if im wrong.
int t/1+t^2 dt
u = 1+t^2
du/dt = 2t
dt = 1/2t du
= int (t/u)(1/2t du)
= int t/2tu du
= 1/2 int t/tu du
= 1/2 int t(tu)^-1 du
= 1/2 int t^0 u^-1 du
= 1/2 [t^1 ln u]+c
= 1/2 ln t (1+t^2)+c (answer)
 
Last edited:
  • #6
13
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could anyone help me here? pls..
 
  • #7
Defennder
Homework Helper
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here it is,pls correct me if im wrong.
int t/1+t^2 dt
u = 1+t^2
du/dt = 2t
dt = 1/2t du
= int (t/u)(1/2t du)
= int t/2tu du
= 1/2 int t/tu du
= 1/2 int t(tu)^-1 du
= 1/2 int t^0 u^-1 du
= 1/2 [t^1 ln u]+c
= 1/2 ln t (1+t^2)+c (answer)
Cancel out t in this step.
 
  • #8
13
0
u mean remove the t? so it will become 1/2u?
here,
= int 1/2u du
= int u^-1/2 du
= 1/2 int u^-1 du
=1/2 [ln u]+c
= 1/2 ln (1+t^2)+c (answer)
am i correct? btw if we remove t,it will become 1/2u right since it was 1t/2tu?
 
  • #9
Defennder
Homework Helper
2,591
5
Yes, that is correct.
 
  • #10
13
0
thank you! :)
i got one more question,
differentiate y= 2m e^mt/cos 2m
is it dy/dt or dy/dm?
2m e^mt,
e^mt if differentiate = e^mt or me^mt?
 
  • #11
Defennder
Homework Helper
2,591
5
I can't read what you are writing here, is it supposed to be [tex]y = \frac{2me^{mt}}{cos(2m)}[/tex]?

Is m a constant or function of t?

As for your 2nd question, it is true that [tex]\frac{d}{dt} \ e^{mt} = me^{mt}[/tex].
 
  • #12
13
0
it is correct except the cos have no bracket, cos2m
i have no idea,im having trouble to decide whether it is dy/dm or dy/dt
 
  • #13
Defennder
Homework Helper
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5
Is m a function of t? Secondly what are you differentiating with respect to?
 
  • #14
13
0
here is my answer,do tell whether it is right or wrong.
2e^mt(m cos 2m+cos 2m+2m sin 2m)/(cos 2m)^2
 
  • #15
13
0
just assume it as dy/dt
sorry im not good in english.
im using quotient rule to solve that.
 
  • #16
Defennder
Homework Helper
2,591
5
You haven't clarified this question: Is 'm' a constant? Or is it a function of t?
 

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