Find the values of a>0 for which the improper integral $\int_{0}^{\infty}\frac{\sin x}{x^{a}} $ converges .
38567
Convergence $I=\int_0^\infty \frac{\sin x}{x^s}dx$
65982
Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
147608
Cauchy principle value of $\int_{-\infty}^{\infty}\sin(x)/(x-a)dx$
23368
Does $\int_1^2\frac{\sin{x}}{\log{x}} \, dx$ converge?
8934
How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?
93071
Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$?
53885
$\forall a > 0$ $\sum_{n=1}^{\infty} f(na)$ is convergent. Prove that $\int_{0}^{\infty}f(x) dx$ is convergent.
83966
Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?
86923
Evaluating the integral $\int_0^\infty \frac{x \sin rx }{a^2+x^2} dx$ using only real analysis
126046
solving the integral $ \int_0^\infty \dfrac{\sin xt}{x(x^2+1)} dx $
117264
Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$
117486
Limit of uniformly continuous functions with convergent improper integrals.
21390
How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$.
72235
Finding the convergence interval of $\sum_{n=0}^\infty\frac{n!x^n}{n^n}$.
69348
Prove that $\int \limits _{0}^{\infty}\frac{e^{-2x}-e^{-ax}}{x}\text{d}x$ converges for any $a>0$
88792
Convergence of $\int_0^\infty $sin$ (x^p) dx$
106087
Finding $\lim_{n \to \infty} \int_1^a \frac{n}{1+x^n} \, dx$