# Integration help please

Integrating $$\frac{1}{(1+sinx)}$$

i just started learning Integration last week so not exactly sure how to approch this type of question.

## Answers and Replies

Do you know how to integrate 1/sinx?

no this is the first time i have seen where a trigonometric function is on the denominator

but now that i think about it

sinx = $$\sqrt{1-cos^2x}$$
and arcsin was equal to $$\frac{1}{((1-x^2)}$$

so i guess i could use the U substituition method
and then the answer would be...arcsin(cosx)??? im not too sure

Last edited:
Dick
Science Advisor
Homework Helper
No, no arcsin. But you might want to try multiplying numerator and denominator by (1-sin(x)). It may look more familiar.

Last edited:
daniel_i_l
Gold Member
You could also try the subsitution u = tan(x/2). It looks a little messy but everything cancels out.

well im not sure if im doing the right thing but here goes....

sinx = $$\frac{2tan(\frac{x}{2})}{1+tan^{2}(\frac{x}{2})}$$

soo then i symplify the equation so that it is

$$\frac{1+tan^{2}(\frac{x}{2})}{1+tan^{2}(\frac{x}{2})+2tan(\frac{x}{2})}$$

the i used u = tan$$(\frac{x}{2})$$

so i get $$\frac{1+u^{2}}{(u+1)^{2}}$$

What should i do from here or is this the right way at all?

Dick
Science Advisor
Homework Helper
It looks to me like you are taking the long way around. Try multiplying numerator and denominator of your original problem by (1-sin(x)). You get (1-sinx)/cos^2(x). If you split that into two integrals you shouldn't have any problem with either of them.

daniel_i_l
Gold Member
Dick solution is quicker in this case but to integrate things like
1/(1+cosx+sinx) the substitution u=tan(x/2) is good.
But notice that it isn't x = tan(u/2) but rather u=tan(x/2). In order to get this into something the the example I gave you can show with so trig identities that if u=tan(x/2) then:
dx = 2du/(1+u^2)
sinx = 2u/(1+u^2)
cosx = (1-u^2)/(1+u^2)
If you substitue all that you the (1+u^2)s candel out and you get some rational function which you can solve with the typical rational function method (breaking it into elementry functions...)

wow by the way i got the answer using what dick said its actually pretty easy once u break it up...now im gonna try Daniels question gonna see if i can get those now :) thnx alot for the help by the way
the answe was tanx - secx +c