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    The integral of 1 (x^2 + 2) dx can be approached using trigonometric substitution, as it resembles the standard integral form for arctangent A common substitution is x = √2 * tan (θ), which simplifies the integral to a form that allows for straightforward integration
  • What is the Integral of -e^ (-x)? - Physics Forums
    The integral of -e^ (-x) is derived using u-substitution, where u = -x, leading to the result -e^ (-x) + C The negative sign arises because the derivative of -x is -1, thus requiring division by -1 during integration The discussion emphasizes that integration can be viewed as the reverse of differentiation, which simplifies the process Some participants clarify that the method of
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    The integral of 1 (x^2 + 1) dx can be solved using the direct formula, yielding arctan (x) + C Substitution methods were discussed, including u = x^2 + 1 and trigonometric substitution with x = tan (θ), but these approaches led to complications with the variable x remaining in the equation Some participants suggested that recognizing the integral as a standard form could simplify the
  • How can the formula for integrating 1 (x^2+y^2)^(3 2) be derived?
    The discussion focuses on deriving the integral of 1 (x^2+y^2)^ (3 2), emphasizing the need for a clear understanding of the derivation process rather than just the formula A suggested approach involves using trigonometric substitution, specifically x = y*tan (θ), which simplifies the integral significantly Participants highlight that many integration formulas arise from initial





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