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Question Number 43342 by pieroo last updated on 10/Sep/18

$$\mathrm{using}\mathrm{the}\mathrm{substitution}\mathrm{u}=\mathrm{x}+2,\mathrm{evaluate}{\int }_1^2\frac{\mathrm{x}-1}{{(\mathrm{x}+2)}^4}$$

Answered by $@ty@m last updated on 10/Sep/18

$$\underset{3}{\stackrel{4}{\int }}\frac{(u-2)-1}{u^4}du$$$$=\underset{3}{\stackrel{4}{\int }}\frac{u-3}{u^4}du$$$$=\underset{3}{\stackrel{4}{\int }}(\frac{1}{u^3}-\frac{3}{u^4})du$$$$\text{Missing left or extra right}$$$$=(\frac{1}{32}-\frac{1}{64})-(\frac{1}{18}-\frac{1}{27})$$$$=\frac{1}{64}-\frac{1}{54}$$$$=\frac{-5}{1728}$$

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