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# Integration

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1. Hi i am trying to integrate 1/(5+4cosx). when i make a substitution t=tan(x//2)
i get 2/3arctan(3tan(x/2))+c so when i use the limits 2Pi/3 and 0 to evaluate i get 0.92 radians which is a wrong answer.
when i make substitution t=1/3tan(x/2) i get 2/3arctan(1/3tan(x/2)) so as a result i end up with 0.35 radians which the book says is right.
Can anyone explain why having followed the correct procedure i get wrong answer. I have checked so many times that i haven't made any algebraic mistake when i made substitution t=tan(x/2)

Also if the choice t=tanx/2 alone is wrong while evaluating the integrals, is there any way to initially guess the value of "a" when making substitution t=a*tanx/2
2. (Original post by Merdan)
Hi i am trying to integrate 1/(5+4cosx). when i make a substitution t=tan(x//2)
i get 2/3arctan(3tan(x/2))+c so when i use the limits 2Pi/3 and 0 to evaluate i get 0.92 radians which is a wrong answer.
when i make substitution t=1/3tan(x/2) i get 2/3arctan(1/3tan(x/2)) so as a result i end up with 0.35 radians which the book says is right.
Can anyone explain why having followed the correct procedure i get wrong answer. I have checked so many times that i haven't made any algebraic mistake when i made substitution t=tan(x/2)

Also if the choice t=tanx/2 alone is wrong while evaluating the integrals, is there any way to initially guess the value of "a" when making substitution t=a*tanx/2
Worked fine when I did it.

I suspect an algebraic slip when working with your fractions. Not got time myself just now, but post your working and someone can check it through.
3. You must have just made a mistake when putting the limits is.
Why didn't you just use your t limits instead of putting the x limits in?

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