Consider the quadratic expression .

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the quadratic expression

x^{2}-4x+7

. (i) Rewrite

x^{2}-4x+7

in the form

(x-h)^{2}+k

, where

h

and

k

are real numbers. (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.

Related theory

Inverse Trigonometric Functions
Trigonometric Functions
Algebraic Manipulation
Standard algebraic integrals
Functions
Solving by completing the square
Quadratic Equations
Integration by Substitution

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