2020HSCMultiple choice

Q6

1 mark

Question

Which expression is equal to $\displaystyle\int\frac{1}{x^2+4x+10}\,dx$ ?

A. $\dfrac1{\sqrt6}\tan^{-1}\left(\dfrac{x+2}{\sqrt6}\right)+c$
B. $\tan^{-1}\left(\dfrac{x+2}{\sqrt6}\right)+c$
C. $\dfrac1{2\sqrt6}\ln\left|\dfrac{x+2-\sqrt6}{x+2+\sqrt6}\right|+c$
D. $\ln\left|\dfrac{x+2-\sqrt6}{x+2+\sqrt6}\right|+c$

Try the question before revealing the answer.

Syllabus alignment

Calculus

Further IntegrationApply substitution, partial fractions, integration by parts and recurrence relationships to theoretical and practical problems.

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