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Calculate this integral: \int {\frac{1}{6-0.5y}} dy.

Question:

Calculate this integral:{eq}\int {\frac{1}{6-0.5y}} dy {/eq}.

Answer and Explanation:


In this problem, we need to calculate this integral:{eq}\int {\frac{1}{6-0.5y}} dy\\ \mathrm{Apply\:u-substitution:}\:u=6-0.5y\\ \Rightarrow \:du=-0.5dy\\ =\int \:-\frac{1}{0.5u}du\\ \mathrm{Use\:the\:integral}:\quad \int \:\frac{1}{u}du=\ln \left(\left|u\right|\right)\\ =-2\ln \left|u\right|+c\\ \mathrm{Substitute\:back}\:u=6-0.5y\\ =>-2\ln \left|6-0.5y\right|+C {/eq}


Learn more about this topic:

Indefinite Integral: Definition, Rules & Examples

from Calculus: Tutoring Solution

Chapter 7 / Lesson 14
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