The value of $\int\limits_{0}^{20\pi} (\sin^4 x + \cos^4 x) dx$ is equal to:

Let [.] denote the greatest integer function. Then the value of $\int\limits_{0}^{3} \left( \frac{e^{x} + e^{-x}}{[x]!} \right) dx$ is :

Let [.] denote the greatest integer function. Then

$$ \int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( \frac{12(3+[x])}{3+\left[\sin x\right]+\left[\cos x\right]} \right) dx $$
is equal to :

Let $f$ be a polynomial function such that $f\left(x^2+1\right)=x^4+5 x^2+2$, for all $x \in \mathbb{R}$.

Then $\int\limits_0^3 f(x) d x$ is equal to