Intuitively, why does $\int_{-\infty}^{\infty}\sin(x)dx$ diverge?
68866
Is $\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$ divergent or convergent?
118330
How do we know what the integral of $\sin (x)$ is?
8934
How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?
1668
Mathematica complaints that convergent integral diverges
60572
Computing $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x$ with residue calculus
34650
Explain why $\int_0^\infty\frac{\sin{4x}}{x}\prod\limits_{k=1}^n \cos\left(\frac{x}{k}\right) dx\approx\frac{\pi}{2}$
119209
Differentiation wrt parameter $\int_0^\infty \sin^2(x)\cdot(x^2(x^2+1))^{-1}dx$
96191
Integral $\int_0^{\infty} \sin(x^2)/x^2\,dx$
13674
Divergence of an improper integral
61495
Why does an integral change signs when flipping the boundaries?
19962
Why is $\infty \cdot 0$ not clearly equal to $0$?
99809
Show that$\displaystyle\sum_{n=1}^\infty\frac{\sin( nz)}{n}$ diverges if $\mathfrak{Im} \,(z)\neq0$
107351
Evaluate the improper integral $\int_{0}^{\infty}{f(x)-f(2x)\over x}dx$, where $\lim_{x \to \infty} f(x) = L$
158147
Calculating $\int_{-\infty}^{\infty}\frac{\sin(ax)}{x}\, dx$ using complex analysis
130967
How to show that $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(4x)\cdots\sin(2^kx)\over x^{k+1}}\mathrm dx=2^{0.5(k^2-k-2)}\pi?$
10547
$\int_0^\infty \frac{\sin(x^2+ax)}{x}\,dx$ converges
79299
Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$