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Calculus/integral problem

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Expert: Alon Mandes - 1/12/2010


Question
hi alon

the question asks to calculate the integral of x^2/(x^2+1)^2 dx

thanks

Answer
1st of all , let's pay attention for 2 major things :
1. { Arctan(x) }' = 1/(1+x^2)
2. { x/(1+x^2) }' = (1-x^2)/(1+x^2)^2
Now, x^2/(x^2+1)^2 can be written as (1/2)[1/(1+x^2) - (1-x^2)/(1+x^2)^2] . Therefore,
Integral of  x^2/(x^2+1)^2 dx = (1/2)[ Arctan(x) - x/(1+x^2)^2 ] .

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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