Question

entegral tagx =?
........................................................................................................................................

Answer 1

Answer:

1. 1. Proof
2. Strategy: Make in terms of sin's and cos's; Use Subtitution.
4. (integral) tan x dx = (integral) sin x
5. cos x dx
6. set
7.  u = cos x.
8. then we find
9.  du = - sin x dx
10. substitute du=-sin x, u=cos x
12. (integral) sin x
13. cos x dx = - (integral)
14. (-1) sin x dx
15. cos x
17. = - (integral) du
18. u
19. Solve the integral
21. = - ln |u| + C
23. substitute back u=cos x
25. = - ln |cos x| + C
26. Q.E.D.

Step-by-step explanation:

Answer 2

integral of tanx is log (cosx) is the right answer