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#1 2018-12-17 20:23:07
- Zeeshan 01
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Integration
Integration of (1/(1+sinx+cosx)) dx by letting tanx/2=z
I used this formulas 2cos^2x/2=1+cosx
And sinx=2sinx/2cosx/2
Malik
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#2 2018-12-17 21:23:20
- Bob
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Re: Integration
hi Zeeshan 01
Post in 'Help' if you want someone to help you with a problem.
Post in 'Exercises' if you have a problem that you can do and want to challenge others.
I'll assume you want help.
Using
is a way that someone has found out that helps with some integrals. If it works then it shouldn't matter why you choose this route. After all, some integrals can be 'done' just by inspection.
Start by showing that
Substitute and simplify.
Even using this 'trick', it's not an easy integral . You'll find it involves log base e.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2018-12-17 21:34:54
- Zeeshan 01
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Re: Integration
I know these sin and cos formulas but these are not useable in my question.use sin and cos formulas (already given in post 1 )
Malik
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#4 2018-12-17 21:38:33
- Zeeshan 01
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Re: Integration
How this becomes (1/2 )sec^2(x/2) /1+tan(x/2)
Malik
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#5 2018-12-17 22:02:16
- Bob
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Re: Integration
Substitute the z expressions:
Then simplify.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#6 2018-12-18 02:54:51
- Zeeshan 01
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Re: Integration
I know your method but i want method in post 4
Malik
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#7 2018-12-18 02:59:57
- Zeeshan 01
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- Registered: 2016-07-22
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Re: Integration
Q. Integration (1/(1+sinx+cosx)) dx
we know sinx=2sinx/2cosx/2 and 2cos^2x/2=1+cosx
So by applying formulas
1/2cos^2(x/2) +2sin(x/2)cos(x/2)
Ok only put formula then
1/2sec^2(x/2) / 1+tan(x/2) how.??
Malik
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#8 2018-12-18 05:04:02
- Bob
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Re: Integration
In post 1
Integration of (1/(1+sinx+cosx)) dx by letting tanx/2=z
So that's what I did.
The alternative method of post 4 does not use z at all.
You now have the presence of a function and it's derivative, so it is directly integrable as ln(function) .
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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