The discussion revolves around integrating trigonometric functions, specifically the integrals of expressions involving cosine and sine. Participants are exploring methods to solve the integrals ∫(1/(1+cos(x)))dx and ∫(x+sin(x))/(1+cos(x))dx.
Several participants have shared their attempts and results, with some providing hints and corrections. There is an ongoing exploration of different methods and identities, but no explicit consensus has been reached regarding the final solutions.
Participants are working within the constraints of a homework assignment, which may limit the information they can share or the methods they can use. There is a noted emphasis on the importance of including arbitrary constants in their final answers.
DivisionByZro said:Show us what you've got. Here are hints:
1 - Use the identity that cos(x)=2*cos(x/2)-1, and then use a simple substitution.
2 - Somewhat similar to the first one.
That identity should beDivisionByZro said:Show us what you've got. Here are hints:
1 - Use the identity that cos(x)=2*cos(x/2)-1, and then use a simple substitution.
2 - Somewhat similar to the first one.
The ∫(x*sec^2(x)).dx + 2∫tan(x/2).dx that you have should be: ∫(x*sec^2(x/2)).dx + 2∫tan(x/2).dx .Redoctober said:I got tan(x/2) + C for the first But nothin for the second .
i did as follows
∫(x+sin(x))/(x+cos(x)).dx
simplified it to
∫(x*sec^2(x)).dx + 2∫tan(x/2).dx
I then i integrated them , i used integration by parts for then right hand integral
Then i finally got
2x*tan(x/2)
Is it correct :D ?
SammyS said:The ∫(x*sec^2(x)).dx + 2∫tan(x/2).dx that you have should be: ∫(x*sec^2(x/2)).dx + 2∫tan(x/2).dx .
Yes, your answer is correct, if you add an arbitrary constant.