MHB Solve My Constant Problem: Integral Sign + -2

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The discussion centers on understanding the role of the -2 in front of the integral sign in a mathematical equation. The clarification provided explains that the -2 can be moved outside the integral, aligning with the previous text. It emphasizes that the numbers marked in yellow do not affect this transformation. The original poster expresses gratitude for the insight, indicating that a fresh perspective helped clarify their confusion. Overall, the exchange highlights the importance of understanding how constants interact with integrals in equations.
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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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