Question

Find: \( \int \frac{2x+1}{\sqrt{x^{2}+10x+9}} d x \)

Answer 1

\(\int\frac{2x+1}{\sqrt{x^2+10x+9}}\)dx

 = \(\int\frac{2x+10-9}{\sqrt{x^2+10x+9}}dx\)

 = \(\int\frac{2x+10}{\sqrt{x^2+10x+9}}dx\) - 9\(\int\frac{1}{\sqrt{(x+5)^2-16}}dx\)

 = 2\(\sqrt{x^2+10x+9}\) - 9log|x + 5 + \(\sqrt{x^2+10x+9}\)| + c