# Homework Help: Integration help please

1. Jul 30, 2007

### gona

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

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

2. Jul 30, 2007

### daveb

Do you know how to integrate 1/sinx?

3. Jul 30, 2007

### gona

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: Jul 30, 2007
4. Jul 30, 2007

### Dick

No, no arcsin. But you might want to try multiplying numerator and denominator by (1-sin(x)). It may look more familiar.

Last edited: Jul 30, 2007
5. Jul 30, 2007

### daniel_i_l

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

6. Jul 30, 2007

### gona

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?

7. Jul 30, 2007

### Dick

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.

8. Jul 30, 2007

### daniel_i_l

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...)

9. Jul 30, 2007

### gona

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