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Calculus/evaluating integrals

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Expert: Alon Mandes - 10/18/2008


Question
Evaluate the integral:  ∫((x2 + x + 1) / (x2 + 1))

Answer
Ok Casy, notice that
∫((x^2+x+1)/(x^2+1))=∫((x^2+1)/(x^2+1))+∫x/(x^2+1)=
∫dx+(1/2)∫2x/x^2+1)dx, right ? it's the same.
As for the forst part : ∫dx=x
As for the second part : we have ∫(f'/f)dx=Ln(f) because 2x=(x^2+1)'.
So the second pard is Ln(x^2+1). & the full answer is:
∫((x^2+x+1)/(x^2+1))dx=x+Ln(x^2+1).

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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