Question

On solving ${\int }_2^3\frac{xdx}{x^2+1}$ we get $\frac{1}{2}\log A+C$ as an answer. What is $A$ in the given answer?

Answer 1

$I={\int }_2^3\left(\frac{xdx}{x^2+1}\right)let{x}^2+1=t\Rightarrow 2xdx=dtifx=2\Rightarrow t=5ifx=3\Rightarrow t=10\therefore I={\int }_5^{10}\left(\frac{1}{t}\right)dt=\left(\frac{1}{2}\right){\left[log|t|\right]}_5^{10}=\left(\frac{1}{2}\right)(log10-log5)=\left(\frac{1}{2}\right)log2+C$