Homework Help

What is the integral `int cos x/(1 + sin x) dx`

user profile pic

xetatheta | Student, Kindergarten | Salutatorian

Posted July 7, 2012 at 7:00 AM via web

dislike 2 like

What is the integral `int cos x/(1 + sin x) dx`

Tagged with calculus, function, integral, math

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 7, 2012 at 7:05 AM (Answer #1)

dislike 1 like

The integral `int cos x/(1 + sin x) dx` has to be determined.

`int cos x/(1 + sin x) dx`

If `1 + sin x = y` , `dy = cos x dx`

=>` int 1/y dy`

=> `ln y`

substitute `y = 1+sin x`

=> `ln(1 + sin x) + C`

The integral `int cos x/(1 + sin x) dx = ln(1 + sin x) + C`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes