Solving Difficult Integral Homework: \int_0^1\frac{ln(1+x)}{1+x^{2}} dx

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SUMMARY

The forum discussion centers on solving the definite integral \(\int_0^1\frac{ln(1+x)}{1+x^{2}} dx\). The user expressed difficulty in finding a suitable method, having attempted various substitutions and integration by parts without success. A key insight shared was the necessity of using a specific identity after making a substitution to simplify the integral. This highlights the importance of recognizing when to apply mathematical identities in integral calculus.

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  • Knowledge of logarithmic functions and their properties
  • Ability to recognize and apply mathematical identities in calculus
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Students studying calculus, particularly those tackling integral problems, as well as educators looking for insights into common student challenges with definite integrals.

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Homework Statement



I'm stuck with this definite integral : \int_0^1\frac{ln(1+x)}{1+x^{2}} dx

Homework Equations



The various "standard integrals".

The Attempt at a Solution



I just don't know where to start, or how to do it. I tried various substitutions but none of them worked; I also tired doing it by parts but that didn't work either.
 
Last edited:
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Okay, I got that. Thanks.
I knew of the identity, but didn't know I'd have to use it after making a substitution.
 

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