Calculus/integrals

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Expert: Alon Mandes - 5/6/2009


Question
find the integral of ln(x^2+1) using integration by parts.

Can you please explain how this can be done as it is not a function multiplied by a function. Otherwise should the substitution method be used?

Answer
Integration by parts rule : ∫u'(x)V(x)dx=u(x)v(x)-∫u(x)v'(x)dx.
In our case u'(x)=1 & v(x)=Ln(x²+1) , thus :
∫Ln(x²+1) dx = xLn(x²+1)-∫2x²/(x²+1) dx .
All we have to do now is to calculate ∫x²/(x²+1) dx !!
This is simple cuase we know that Arctang(x)'=1/(x²+1). So,
x²/(x²+1) can be written as 1-1/(x²+1), thus :
∫x²/(x²+1) dx = ∫1-1/(x²+1) dx = x-Arctang(x). Now we have :
∫Ln(x²+1) dx = xLn(x²+1)-2x-2Arctang(x).

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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