Question

If $\int \frac{d x}{(x+2)\left(x^{2}+1\right)}=a \log \left|1+x^{2}\right|+b \tan ^{-1} x+\frac{1}{5} \log |x+2|+c$, then

• A. $a =\frac{-1}{10} b =\frac{2}{5}$
• B. $a=\frac{-1}{10} b=\frac{-2}{5}$
• C. $a=\frac{1}{10} \quad b=\frac{2}{5}$
• D. $a=\frac{1}{10} \quad b=\frac{-2}{5}$

Answer 1

Answer: (A)

$\frac{1}{(x+2)\left(x^{2}+1\right)}=\frac{A}{x+2}+\frac{B x+C}{x^{2}+1}$
$A=\frac{1}{5}, B=\frac{-1}{5}, C=\frac{2}{5}$