The function $f(x) = \int \dfrac{x+3}{x^2-9x+20}\,dx$, then $f(x)$ is

If $f(x) = \log(1 + x) - \dfrac{x}{1+x}$, then the values of $x$ for which $f(x)$ is monotonically increasing and monotonically decreasing are respectively.....

The number 28 is divided into two positive parts such that the sum of the cube of one part and the square of the other part is minimum, then the absolute difference between the two parts is

The value of $\int \dfrac{\sin^3 x}{(\cos^4 x + 3\cos^2 x + 1)\tan^{-1}(\sec x + \cos x)}\,dx$ is