## artofspeed 2 years ago hard integral: http://puu.sh/23Ps6

1. hartnn

|dw:1361078522674:dw| do you see why i did that ?

2. artofspeed

isn't this 0.5*integral of dx/(sinx+cosx)?

3. artofspeed

@Joseph91 What do you do next?

4. Joseph91

sorry error

5. hartnn

|dw:1361079028915:dw| |dw:1361079065220:dw|you know the integral of cosec ???

6. hartnn

also , did you get how its sin (x+pi/4) ??

7. artofspeed

yes and yes, thanks!

8. hartnn

that was the hint we used, for your original question, |dw:1361079880505:dw|

9. artofspeed

thanks a lot, i got it! :D

10. hartnn

welcome ^_^

11. artofspeed

I got $\frac{1}{2\sqrt2}*\ln|\csc(2x+\pi/4)-\cot(2x+\pi/4)|$ can anyone check if it's the right answer?

12. hartnn

yes, that seems correct.

13. artofspeed

i tried to integrate on wolfram alpha, it gives me something else. To check if they are equal, I plugged a number for x in both equations, but got different answer.. :O is that normal?

14. hartnn

i think they will be equivalent, with just different form, which value you tried ?

15. artofspeed

x=-10

16. hartnn

-10 what ? degrees or radians ?

17. artofspeed

degree

18. hartnn

i checked, it comes out to be different. also i missed earlier that integral of cosec x is ln |cosec x + cot x|+c and you've typed - *minus*

19. hartnn

but our method is correct, maybe it comes different because of the constant '+c' which might be different for both forms....

20. artofspeed

hey!!! i got it, if i calculate the $\int\limits_{a}^{b}f(x)$ of both equations, it gives the same value if a and b are the same, so it's correct! Also thanks a lot for spending so much time on this, I really appreciate it!

21. hartnn

oh, good! and welcome ^_^