Evaluate the integral 6x-4 x^ 2 +4x+8 ,dx

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

Evaluate the integral ∫6x−4x2+4x+8 dx.\int \frac{6x-4}{x^{2}+4x+8}\,dx. (a) First rewrite the denominator in completed–square form. (b) Hence find the exact value of the integral, expressing your answer in terms of natural logarithm and inverse tangent functions as required.

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