Question

integral of 1/(1+sinx)

Answer 1

try multiplying by (1-sinx)/(1-sinx)

Answer 2

Good suggestion. :)

Answer 3

then it will simplify to
\[\int\limits \sec^2 x - \sec x \tan x\]

Answer 4

From Mathematica 9:\[\int\limits \frac{1}{\sin (x)+1} \, dx=\frac{2}{\cot \left(\frac{x}{2}\right)+1} \]

Answer 5

I was thinking that if you multiply by (1- sinx)/(1-sinx) you would get (1-sinx)/(1-sin^2x) or (1-sinx)/(cos^2(x)) ; If you then break it up like this: 1/cos^2(x) - sinx/cos^2(x), you would have sec^2(x) - sinx/cos^2(x) and then maybe split it into two integrals

Answer 6

so that the first would be the integral of sec^2(x) which would just be tanx. And then the second one you could use a u substitution on, letting cosx = u

Answer 7

so that you would have the integral of (1/u^2) du

Answer 8

so that would give you -u^(-1) or -1/u then since u = cosx, that would be -1/cosx or -secx

Answer 9

but I'm going to look at it again to make sure! My final answer was going to be tanx - secx + C

but I'll double check.

Answer 10

Got the same thing again.