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## #1 2018-12-17 20:23:07

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### 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

M.M.Zeeshan.K

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## #2 2018-12-17 21:23:20

bob bundy
Registered: 2010-06-20
Posts: 8,442

### 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 Bundy

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## #3 2018-12-17 21:34:54

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### 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 )

M.M.Zeeshan.K

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## #4 2018-12-17 21:38:33

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### Re: Integration

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

M.M.Zeeshan.K

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## #5 2018-12-17 22:02:16

bob bundy
Registered: 2010-06-20
Posts: 8,442

### 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 Bundy

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## #6 2018-12-18 02:54:51

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### Re: Integration

I know your method but i want method in post 4

M.M.Zeeshan.K

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## #7 2018-12-18 02:59:57

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 717

### 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.??

M.M.Zeeshan.K

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## #8 2018-12-18 05:04:02

bob bundy
Registered: 2010-06-20
Posts: 8,442

### Re: Integration

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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