If $\int f(x) dx = g(x)$,then $\int f(x) g(x) dx$ is equal to

If the primitive of $f(x) = \pi \sin(\pi x) + 2x - 4$ has the value $3$ for $x = 1$,then the set of $x$ for which the primitive of $f(x)$ vanishes is:

$\int \frac{1}{16 x^{2}+9} d x$ is equal to

$\int \frac{(x^2+1)}{(x+1)^2} dx =$

Find the integral of the function $\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}$.

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