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# Integrate 1 + sinx/cos x

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1. I'm quite stuck on this question: Integrate 1 + sinx/cosx by substitution.
The book also says let u=sin x

Now I was thinking of changing it into sec x + tan x but that didn't get me far

Should I bring cosx to the top?

Sorry btw, I can't use latex so please bear with me!
2. If you substitute then you get , so you get on the denominator. How might you write in terms of ?
3. (Original post by nuodai)
If you substitute then you get , so you get on the denominator. How might you write in terms of ?
U^2

e: i got negged coz i got it wrong
4. So I got 1 + sinx du/cos^2x?
5. (Original post by This Honest)
U^2
No. so - try again!

(Original post by This Honest)
So I got 1 + sinx du/cos^2x?
Not quite, you should have . Now put this in terms of .
6. (Original post by This Honest)
So I got 1 + sinx du/cos^2x?
Then use the fact that u= sinx

and cos^2x = 1-sin^2x.
7. (Original post by nuodai)
No. so - try again!

Not quite, you should have . Now put this in terms of .

Then use the fact that u= sinx

and cos^2x = 1-sin^2x.
Alright guys,

I've now got: 1 + u/1-sin^x
8. (Original post by This Honest)
Alright guys,

I've now got: 1 + u/1-sin^x
Write it in terms of ; that still has an in it. You'll notice that you can factorize something that simplifies the expression into something you can integrate.
9. (Original post by This Honest)
I'm quite stuck on this question: Integrate 1 + sinx/cosx by substitution.
The book also says let u=sin x

Now I was thinking of changing it into sec x + tan x but that didn't get me far

Should I bring cosx to the top?

Sorry btw, I can't use latex so please bear with me!
This question can also be easily done without substitution,

Now try to differentiate,
10. integrate: 1 +u/1-u^2 ??
11. (Original post by This Honest)
I'm quite stuck on this question: Integrate 1 + sinx/cosx by substitution.
The book also says let u=sin x

Now I was thinking of changing it into sec x + tan x but that didn't get me far

Should I bring cosx to the top?

Sorry btw, I can't use latex so please bear with me!
12. (Original post by This Honest)
Alright guys,

I've now got: 1 + u/1-sin^x
1+u/1-u^2

remember that u = sinx and that cos^2(x) = 1 - sin^2(x)
13. (Original post by nuodai)
Write it in terms of ; that still has an in it. You'll notice that you can factorize something that simplifies the expression into something you can integrate.
1/1-u
14. (Original post by This Honest)
integrate: 1 +u/1-u^2 ??
Yes, remember you will have to use partial fraction.

15. I GOT IT!

-ln!1-sinx! + c

can't find modular signs on keyboard \$

Thanks everyone for the help
16. (Original post by This Honest)
integrate: 1 +u/1-u^2 ??
have you learnt the integration rule, where if you differentiate the denominator, you get the value that appears in the numerator. hence ln(your original function)

have you come across this before?

this could prove useful here.

someone else correct me if im wrong

WHOOPS PARTIAL FRACTIONS ARE THE WAY FORWARD
17. (Original post by raheem94)
Yes, remember you will have to use partial fraction.

I didn't quite understand your method but thanks anyways
18. (Original post by blacklistmember)
Why post then?
19. (Original post by James A)
have you learnt the integration rule, where if you differentiate the denominator, you get the value that appears in the numerator. hence ln(your original function)

have you come across this before?

this could prove useful here.

someone else correct me if im wrong

WHOOPS PARTIAL FRACTIONS ARE THE WAY FORWARD
OHHHHHHH YEAHHHHHHH!

The book said "by sub" so my mind was only on sub and nothing else
20. (Original post by raheem94)
Yes, remember you will have to use partial fraction.

I don't think so.

If it's (1+u)/ (1-u^2) = (1+u)/(1-u)(1+u) = 1/(1-u) = - I of -1/(1-u) then it's a simple f'(u)/f(u) integral.

I think you mis-interpreted .

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Updated: April 1, 2012
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