If $$\mathrm{I}=\int \frac{2 x-7}{\sqrt{3 x-2}} \mathrm{~d} x$$, then $$\mathrm{I}$$ is given by

$$\int \frac{\log \left(x^2+a^2\right)}{x^2} d x=$$

If $$\int x^5 e^{-4 x^3} \mathrm{~d} x=\frac{1}{48} \mathrm{e}^{-4 x^3} \mathrm{f}(x)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration, then $$\mathrm{f}(x)$$ is given by

If $$\mathrm{f}(x)=\int \frac{x^2 \mathrm{~d} x}{\left(1+x^2\right)\left(1+\sqrt{1+x^2}\right)}$$ and $$\mathrm{f}(0)=0$$, then $$\mathrm{f}(1)$$ is