If $$\int \frac{x^3 \mathrm{~d} x}{\sqrt{1+x^2}}=\mathrm{a}\left(1+x^2\right) \sqrt{1+x^2}+\mathrm{b} \sqrt{1+x^2}+\mathrm{c}$$ (where $$\mathrm{c}$$ is a constant of integration), then the value of $$3 \mathrm{ab}$$ is

Let $$f(x)=\int \frac{x^2-3 x+2}{x^4+1} \mathrm{~d} x$$, then function decreases in the interval

If $$\int \frac{\log \left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}} d t=\frac{1}{2}[g(t)]^2+c$$, (where $$c$$ is a constant of integration), then $$g(2)$$ is

$$\int \frac{x-3}{(x-1)^3} e^x d x=$$