If $f'(x) = \dfrac{(\sqrt{x}+1)e^{\sqrt{x}}}{\sqrt{x}}$ and $f(0) = e$ then $f(1) = \ldots\ldots\ldots\ldots$

If $f\left(\dfrac{x-1}{x+1}\right) = x + 1$, then $\int f(x)\,dx = \cdots$

If $f(x) = \cos x$, then the value of $\int\dfrac{e^{f(x)}(x\sin^3 x + f(x))}{1 - (f(x))^2}dx = $

$\int\dfrac{x^4 + 1}{x^6 + 1}dx = $