Evaluate: \(\rm \int \frac{2x^3}{(x^2+2)(x^4+1)}dx\)
1
\(\rm \int\frac{2x^3}{(x^2+2)(x^4+1)}dx=\frac{-2}{5}log\left | x^2+2 \right |+\frac{1}{5}log\left | x^4+1 \right |+\frac{1}{5}tan^{-1}x^2+C\)
2
\(\rm \frac{2}{5}log\left | x^2+2 \right |+\frac{2}{5}log\left | x^2+1 \right |+\frac{1}{5}tan^{-1}x^2+C\)
3
\(\rm \frac{-2}{5}log\left | x+2 \right |+\frac{2}{5}log\left | x^2+1 \right |+\frac{1}{5}tan^{-1}x^2+C\)
4
\(\rm \frac{-2}{5}log\left | x^2+2 \right |+\frac{2}{5}log\left | x^2+1 \right |+\frac{1}{5}tan^{-1}x+C\)