Mathematics

Problem

Consider the quadratic expression

x^{2}-4x+7

. a. (i) Rewrite

x^{2}-4x+7

in the form

(x-h)^{2}+k

, where

h

and

k

are real numbers. b. (ii) Without carrying out the complete integration, state which inverse trigonometric function you expect to appear in the evaluation of

\displaystyle\int \frac{dx}{x^{2}-4x+7}

and give a brief justification for your answer.

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