$$\text { If } \int e^{x^2} \cdot x^3 \mathrm{~d} x=e^{x^2} \cdot[f(x)+C]$$ (where $$C$$ is a constant of integration.) and $$f(1)=0$$, then value of $$f(2)$$ will be

$$\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x=$$

$$\int \cos ^3 x e^{\log (\sin x)^2} d x=$$

$$\int \frac{d x}{e^x+e^{-x}+2}=$$