4-5-x-2-x-2-4x-3-3-dx-

Question Number 537 by kth last updated on 25/Jan/15

\int_{4}^{5} \frac{x - 2}{{(x^{2} - 4 x + 3)}^{3}} d x

Answered by Vishal last updated on 25/Jan/15

l e t x^{2} - 4 x + 3 = t t h e n (x - 2) d x = \frac{d t}{2}

\Rightarrow \int_{t_{1}}^{t_{2}} \frac{d t}{2 {(t)}^{3}} = \frac{1}{2} \int_{3}^{8} t^{- 3} d t = \frac{- 1}{4} {[\frac{1}{t^{2}}]}_{3}^{8}

\Rightarrow \frac{- 1}{4} [\frac{1}{64} - \frac{1}{9}] = \frac{- 1}{4} (\frac{- 55}{576}) = \frac{55}{2304}

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