## amorfide 2 years ago integrate 1/3x+2

1. amorfide

|dw:1350485381398:dw|

2. amorfide

is this right?

3. amorfide

@ParthKohli

4. Zarkon

+c

5. amorfide

that stupid freaking C lol

6. ParthKohli

Yeah, that is and then a constant... don't forget the constant.

7. amorfide

parth tell me how to integrate this one...

8. amorfide

|dw:1350485522236:dw|

9. ParthKohli

$2\int{dx \over x^2 + 3}$That's tricky stuff: trig substitution.

10. amorfide

i literally cant do it :P

11. ParthKohli

no no no... wait

12. ParthKohli

not trig substitution

13. amorfide

if it was 2/x²+1 it would be a trig function

14. ParthKohli

@Zarkon Please, if you might be able to help?

15. Zarkon

you can use trig sub

16. ParthKohli

Got it

17. ParthKohli

How?

18. Zarkon

$x=\sqrt{3}\tan(\theta)$

19. amorfide

huh explain?

20. ParthKohli

Oh, yup...that makes sense.

21. ParthKohli

@amorfide Trigonometric substitution! Search it on Google.

22. Zarkon

if you have $\int\frac{2}{x^2+1}dx$ then just recall that $$\displaystyle\frac{d}{dx}\tan^{-1}(x)=\frac{1}{x^2+1}$$ and therefore $\int\frac{2}{x^2+1}dx=2\cdot\tan^{-1}(x)+c$ if you want $\int\frac{2}{x^2+3}dx$ then, if you want, you can use the substitution I gave above

23. amorfide

so if 2/(x²+1) = 2tan^-1(x/root1) all over root 1 2/(x²+3) = |dw:1350487017539:dw|

24. Zarkon

+c ;)

25. amorfide

LOL thank you! always forget the C... would i lose a mark for not putting +c if i do not need to figure out C?

26. Zarkon

yes

27. amorfide

ahh okay, thank you :D

28. Zarkon

there will be a time in the future when you will find a value for C. Particularly when doing initial value differential equations