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

Zeeshan 01
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Registered: 2016-07-22
Posts: 719

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
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Registered: 2010-06-20
Posts: 8,447

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 smile

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

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 719

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: 719

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
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Registered: 2010-06-20
Posts: 8,447

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 smile

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

Zeeshan 01
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Registered: 2016-07-22
Posts: 719

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: 719

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
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Registered: 2010-06-20
Posts: 8,447

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 smile

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