Goten77 3 years ago integral question below

1. Goten77

$\int\limits_{}^{}\frac{ x }{ \sqrt{x ^{2}+4x+3}}dx =\int\limits \frac{ x }{\sqrt{ (x+2)^{2}-1}}$

2. Goten77

i got a little bit more work so far hold on

3. Goten77

x+2 = sec(x) is what im told to do.. and i get this then x= sec(x)-2

4. hartnn

i would have written x = A d/dx (x^2+4x+3) + B find A,B , then separate the denominator.... but i still have to figure out the best way....

5. Goten77

dx=sec(beta)tan(beta)d(beta) ^ yes i forgot to change betas and x symbols but .... ya kno what i meant XD

6. hartnn

if you are told to substitute that , then did u get (sec -2) sec ?

7. Goten77

$\int\limits_{}^{}\frac{ \sec(u)-2 }{ \sqrt{\sec(u)^{2}}-1 }\sec(u)\tan(u)du$

8. hartnn

the -1 is inside the sqrt sign and sec^2 -1 =... ?

9. Goten77

|dw:1356259318789:dw|

10. Goten77

|dw:1356259400708:dw|

11. hartnn

[sec (theta)-2 ] not sec(theta-2)

12. Goten77

|dw:1356259463598:dw|

13. hartnn

14. hartnn

both integrals are standard

15. Goten77

|dw:1356259538572:dw|

16. Goten77

and then plug back in the u substitution.....right?

17. hartnn

yeah...the final answer will not look cute....

18. Goten77

its a mess.... but man not sure y this calculus 2 entrance paper has this as a question..... its just long

19. hartnn

long .... ? u might have started integration.....

20. hartnn

u got this in just few steps...

21. Goten77

well i had a few friends tell me bout this and how they couldn't get it... but then when i noticed there plugin in all kinds of random things for u substitution i noticed how horribly wrong they did it....but also u was kinda given so.... XD not sure how this is a hard question but there making it required at our ACC to do this ... i guess its to see how well our cal 1 professors taught us or to see if kids can follow directions..... i mean come on ur given all the hard things to solve

22. Goten77

btw could this be done using integration by parts? * i havent dont this for like 2 years and forgot really how it works... but soemthing like this* |dw:1356260012904:dw|

23. hartnn

this particular example ? no, for integration by parts, u need 2 different functions, like trigo and algebraic or expo. and trigo. .... this only has algebraic b4 substitution and trigo. after substitution....so no.

24. Goten77

hmm ....yep i totally forgot all that XD oh well ill just have to refresh on it when i do cal 2