$\int {\frac{{{e^{5\log x}} - {e^{4\log x}}}}{{{e^{3\log x}} - {e^{2\log x}}}}\;dx} = $

$\int 3^{-\log _9 x^2} d x=$

If $\frac{d}{d x} f(x)=4 x^3-\frac{3}{x^4}$ such that $f(2)=0$,then $f(x)$ is equal to

Integrate the function: $\sqrt{1-4x^2}$

Find the integral of the function $\frac{1-\cos x}{1+\cos x}$.

If $f\left( \frac{3x - 4}{3x + 4} \right) = x + 2, x \ne -\frac{4}{3}$,and $\int f(x) dx = A \log |1 - x| + Bx + C$,then the ordered pair $(A, B)$ is equal to: (where $C$ is a constant of integration)