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solve integral step by step with explanations of an integral with upper limit of 9 and lower of 4 2 sqrt x 3 x

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solve integral step by step with explanations of an integral with upper limit of 9 and lower of 4. (2-sqrt(x))/(3-x)

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Answer to a math question solve integral step by step with explanations of an integral with upper limit of 9 and lower of 4. (2-sqrt(x))/(3-x)

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109 Answers

$=\int _{-1}^{-6}-\frac{2-\sqrt{-u+3}}{u}du$

$=-\int _{-6}^{-1}-\frac{2-\sqrt{-u+3}}{u}du$

$=-(-\int _{-6}^{-1}\frac{2-\sqrt{-u+3}}{u}du)$

$=-(-\int _{-6}^{-1}\frac{2}{u}-\frac{\sqrt{-u+3}}{u}du)$

$=-(-(\int _{-6}^{-1}\frac{2}{u}du-\int _{-6}^{-1}\frac{\sqrt{-u+3}}{u}du))$

$=-(-(-2\ln(6)-(\sqrt{3}\ln(2-\sqrt{3})-2)))$

$=-2\ln(6)-\sqrt{3}\ln(2-\sqrt{3})+2$

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