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fiziksfun
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Can someone explain to me why \int\frac{x}{x^2+1} = \frac{1}{2}ln(x^2+1) WHERE DOES THE ONE HALF COME FROM ?
Why is the Constant 1/2 Used in Evaluating Integrals and Differentials?
- Thread starter fiziksfun
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- Differentials Integrals
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Homework Help Overview
The discussion revolves around understanding the appearance of the constant 1/2 in the evaluation of the integral \(\int\frac{x}{x^2+1}dx\), specifically questioning its derivation and significance in the context of calculus.
Discussion Character
- Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants explore the relationship between the integral and its derivative, with some suggesting that taking the derivative of the result could clarify the presence of the constant. Others mention using substitution as a method to evaluate the integral.
Discussion Status
The conversation includes attempts to guide the original poster towards understanding through hints about differentiation and substitution. However, there is a noted frustration from the original poster regarding the clarity of the responses, indicating that the discussion is ongoing without a clear resolution.
Contextual Notes
There is a suggestion that the original poster may not be fully prepared to apply the substitution method effectively, and a reminder about the importance of the chain rule in calculus is mentioned. The discussion reflects varying levels of understanding among participants.