Solve My Constant Problem: Integral Sign + -2

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SUMMARY

The discussion centers on the integration process involving a negative coefficient (-2) in front of the integral sign. The transformation of the equation is clarified, indicating that the negative sign can be factored out of the integral, specifically from the term $e^{-x}$. The participants confirm that the yellow-marked twos do not affect this transformation, and the initial confusion stemmed from an incomplete equation. Acknowledgment of the need for a fresh perspective is noted as beneficial in resolving the misunderstanding.

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I don’t understand how the second (-2) (in front of the integral sign) gets into the equation. Can you please help me?View attachment 8766
 

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Hi, and welcome to the forum.

It's not clear to me which equality your question is about. Besides the line "Not counting..." you post contains a single equality, the one with yellow marks in the left-hand side. This equality is correct because it simply moves the minus in front of $e^{-x}$ outside the integral, just like the text in the previous line says. Twos marked in yellow don't participate in this transformation. As for the first line, it's only half of an equation, so it is not clear what is being claimed about it.
 
Hi Evgeny,

Thanks, I reviewed it again and it seems I just needed "fresh eyes/mind" to look at the problem. Thanks again!
 

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