Challenging +1.2 This is a standard Further Maths integration requiring completing the square to get x²+6x+13=(x+3)²+4, then using the standard result ∫1/√(u²+a²)du = ln|u+√(u²+a²)|+c. The substitution and evaluation at limits is routine, though the algebraic manipulation to reach ln(p+q√2) form requires care. More mechanical than insightful for FP1 level.
In this question you must show detailed reasoning.
Find \(\int_{-1}^{11} \frac{1}{\sqrt{x^2 + 6x + 13}} dx\) giving your answer in the form \(\ln(p + q\sqrt{2})\) where \(p\) and \(q\) are integers to be determined. [7]
In this question you must show detailed reasoning.
Find $\int_{-1}^{11} \frac{1}{\sqrt{x^2 + 6x + 13}} dx$ giving your answer in the form $\ln(p + q\sqrt{2})$ where $p$ and $q$ are integers to be determined. [7]
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q5 [7]}}