If $u$ and $v$ are functions of $x$, then $\int \dfrac{1}{v^3}\left(uv\dfrac{du}{dx} - u^2\dfrac{dv}{dx}\right)dx = $

If $f(x) = |5x - 3|$ is defined on interval $[0, 1]$, then the value of $\int_0^1 f(x)\,dx$ is...

The value of integral $\int_0^\infty \dfrac{1}{1 + e^x}\,dx$ is...

If $f(x)$ is an antiderivative of $\dfrac{x + 1}{\sqrt{x - 1}}$ with respect to $x$, then value of $f(5) - f(2)$ is...