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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 740

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

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,524

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 Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 740

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 )

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 740

How this becomes (1/2 )sec^2(x/2) /1+tan(x/2)

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,524

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 Bundy

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 740

I know your method but i want method in post 4

M.M.Zeeshan.K

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 740

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.??

M.M.Zeeshan.K

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,524

In post 1

Zeeshan 01 wrote:

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 Bundy

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