Homework Help

What is antiderivative of y=sinx/(1+cosx)?

user profile pic

luvgoj | Student, Undergraduate | Honors

Posted July 21, 2013 at 3:02 PM via web

dislike 1 like

What is antiderivative of y=sinx/(1+cosx)?

1 Answer | Add Yours

Top Answer

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 21, 2013 at 3:26 PM (Answer #1)

dislike 1 like

You need to evaluate the anti-derivative of the given function, hence, you need to evaluate the indefinite integral, such that:

`int ydx = int sinx/(1+cosx) dx`

You should come up with the following substitution to evaluate the integral, such that:

`1 + cos x = t => -sin x dx = dt => sin x dx = -dt`

Replacing the variable, yields:

`int sinx/(1+cosx) dx = int (-dt)/t = -ln |t| + c`

Replacing back `1 + cos x` for `t` yields:

`int sinx/(1+cosx) dx = -ln|1 + cos x| + c`

`int sinx/(1+cosx) dx = ln|1 + cos x|^(-1) + c`

`int sinx/(1+cosx) dx = ln|1/(1 + cos x)| + c`

Hence, evaluating the anti-derivative of the given function, yields `int sinx/(1+cosx) dx = ln|1/(1 + cos x)| + c.`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes