Evaluate the definite integral $\int_{4}^{5} e^{x} \, dx$.

$\int_0^1 \tan^{-1} x \, dx =$

Let $n$ be a positive integer. For a real number $x$,let $[x]$ denote the largest integer not exceeding $x$ and $\{x\}=x-[x]$. Then,$\int \limits_1^{n+1} \frac{(\{x\})^{[x]}}{[x]} d x$ is equal to

$\int_{\pi / 4}^{\pi / 3} \frac{\cos x-\sin x}{\sin 2 x} d x=$

$\int\limits_0^3 \left( \frac{1}{\sqrt{x^2 + 4x + 4}} + \sqrt{x^2 - 4x + 4} \right) dx =$

Evaluate the definite integral: $\int_0^{\pi^2 / 4} (2 \sin \sqrt{x} + \sqrt{x} \cos \sqrt{x}) \, dx$