Integral of t/1+t^2

1. May 19, 2008

rojak44

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..

2. May 19, 2008

exk

How did you get your answer?

3. May 19, 2008

rojak44

im using the integration using substitution..
im confuse right now.. can anyone give me the full calculation or what method i should use.

4. May 19, 2008

rock.freak667

$$\frac{t}{1+t^2} dt$$

Let $u=1+t^2$ what is $\frac{du}{dt}$? then what is dt in terms of du?

5. May 19, 2008

rojak44

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: May 19, 2008
6. May 20, 2008

rojak44

could anyone help me here? pls..

7. May 20, 2008

Defennder

Cancel out t in this step.

8. May 20, 2008

rojak44

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. May 20, 2008

Defennder

Yes, that is correct.

10. May 20, 2008

rojak44

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. May 20, 2008

Defennder

I can't read what you are writing here, is it supposed to be $$y = \frac{2me^{mt}}{cos(2m)}$$?

Is m a constant or function of t?

As for your 2nd question, it is true that $$\frac{d}{dt} \ e^{mt} = me^{mt}$$.

12. May 20, 2008

rojak44

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. May 20, 2008

Defennder

Is m a function of t? Secondly what are you differentiating with respect to?

14. May 20, 2008

rojak44

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. May 20, 2008

rojak44

just assume it as dy/dt
sorry im not good in english.
im using quotient rule to solve that.

16. May 21, 2008

Defennder

You haven't clarified this question: Is 'm' a constant? Or is it a function of t?

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