Arc tangent antiderivative after completing the square

Arc tangent antiderivative after completing the square

IB Year 6 | Grade 12

5 marks

Find \(\displaystyle\int\frac1{x^2+4x+8}\,\mathrm dx\).[5]

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Answer:\(\frac12\arctan\!\left(\frac{x+2}{2}\right)+C\)

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