Prove the Integral of $\frac{1}{x}$ is not a Rational Function
127605
What are some methods to show $\log$ is not a rational function?
21843
Proving a function is not Riemann integrable
130935
Evaluating $\int_{0}^{1}\frac{x-1}{(x+1)\ln x} dx $
69978
Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
33097
Proving an inequality without an integral: $\frac {1}{x+1}\leq \ln (1+x)- \ln (x) \leq \frac {1}{x}$
57686
Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
94244
$\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$
104094
Integral of $\frac{1}{(1+x^2)^2}$
104691
Integration of $\int_{0}^{1} \frac{x^k}{1-x} dx$
34762
Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?
117751
An integral of a rational function of logarithm and nonlinear arguments
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
105707
A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
10675
Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
38515
Integral of $\frac{1}{x^4+1}$
24716
$\int_0^\infty\frac{\log x dx}{x^2-1}$ with a hint.