using-the-substitution-u-x-2-evaluate-1-2-x-1-x-2-4-

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

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

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

\underset{3}{\int^{4}} \frac{(u - 2) - 1}{u^{4}} d u

= \underset{3}{\int^{4}} \frac{u - 3}{u^{4}} d u

= \underset{3}{\int^{4}} (\frac{1}{u^{3}} - \frac{3}{u^{4}}) d u

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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