Help Calculating Definite Integral

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SUMMARY

The discussion focuses on calculating the definite integral of the function (2(x)^2)/((x+1)((x)^2+1)) from 0 to 1. The correct indefinite integral is established as (1/2)ln2 + ln2 - (pi/4), leading to the conclusion that the final answer simplifies to (3/2)ln2 - (pi/4). Participants emphasize the importance of using partial fractions to decompose the integrand and highlight the necessity of combining like terms to arrive at the correct result.

PREREQUISITES
  • Understanding of definite integrals and their calculations
  • Familiarity with partial fraction decomposition
  • Knowledge of logarithmic properties and simplification techniques
  • Basic algebra skills for combining like terms
NEXT STEPS
  • Study the method of partial fraction decomposition in calculus
  • Learn how to simplify logarithmic expressions effectively
  • Practice solving definite integrals with various functions
  • Review algebraic techniques for combining like terms in expressions
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Students studying calculus, particularly those tackling integration problems, as well as educators looking for examples of integral calculations and algebraic simplifications.

realism877
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Homework Statement



(2(x)^2)/((x+1)((x)^2+1)) from 0 to 1







The indefinite answer is (1/2)ln2+ln2-(pi/4)

How did it get to this answer?(3/2)ln2-(pi/4)
 
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Use partial fractions to write the integrand as
\frac A {x+1}+\frac{Bx+C}{x^2+1}
 
LCKurtz said:
Use partial fractions to write the integrand as
\frac A {x+1}+\frac{Bx+C}{x^2+1}


I did that.

I already have the solution. I'm just trying to figure out where the 3 came from.
 
Oh my! I thought you had a calculus question about integrating. Instead you have an elementary algebra question. See if you can figure out how to combine like terms and make your answer agree with the given answer.
 
realism877 said:
The indefinite answer is (1/2)ln2+ln2-(pi/4)
What do you mean the indefinite answer? Where are the x's?

You will need to show us your work in how you got to your answer. You might have made an error in your work.
 

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