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"url": "https://numbas.mathcentre.ac.uk/api/questions/11753/?format=api",
"name": "Integration by substitution",
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"full_name": "Newcastle University Mathematics and Statistics",
"pk": 697,
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"notes": "\n \t\t<p><strong>20/06/2012:</strong></p>\n \t\t<p>Added tags.</p>\n \t\t<p>Extensively changed the variables in order to simplify the question - quadratics generated which only have complex roots to stop the quadratic being zero in any range.</p>\n \t\t<p>Added Steps prompt about losing a mark. Also added to Steps re using abs.</p>\n \t\t<p>Added required string abs for answer entry.</p>\n \t\t<p>Improved spacing.</p>\n \t\t<p><strong>4/07/2012:<br /></strong></p>\n \t\t<p>In the steps it is explained that the absolute value of the natural logarithm is inputted as ln(abs(x)) however unless steps are revealed it is unclear how to write |x|. Should this information be included in the question somehow?</p>\n \t\t<p><strong>6/08/2012:</strong></p>\n \t\t<p>Information on using ln(abs(x)) included in the statement.</p>\n \t\t<p> </p>\n \t\t",
"licence": "Creative Commons Attribution 4.0 International",
"description": "<p>Find $\\displaystyle I=\\int \\frac{2 a x + b} {a x ^ 2 + b x + c}\\;dx$ by substitution or otherwise.</p>"
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