Spo�t�te:
$$
\lim_{k \to +\infty} \int_0^{+\infty} e^{-kx} \frac{\sin ax}{x}
\dx,\, a \in \Bbb R, \qquad
\lim_{k \to +\infty} \int_0^{+\infty} \frac{e^{-kx}}{1+x^2} \dx,
\qquad
$$

$$
\lim_{k \to +\infty} \int_0^{+\infty}  e^{-x^k}\dx,  \\
\int_0^{1} \frac{\log (1+x)}{x} \dx, \qquad
$$

$$
\int_0^{1} \frac{\log (1-x)}{x} \dx, \qquad
\int_0^{+\infty} \frac{x}{e^x + 1}\dx, \qquad
$$

$$
\int_0^{+\infty} e^{-x} \cos \sqrt{x} \dx.
$$
