$$\[ 4 x^{2}+4 x+17 \equiv(2 x+p)^{2}+q \]$$ where $$\(p\)$$ and $$\(q\)$$ are integers. Hence use algebraic integration to show that $$\[ \int_{\frac{1}{3}}^{1} \frac{8 x+5}{\sqrt{4 x^{2}+4 x+17}} d x=k+\frac{1}{2} \ln k \]$$ where $$\(k\)$$ is a rational number to be determined. (5)

Answer:

Knowledge points:

Solution: