My conjecture $\int_{0}^{1}{x^n-1 \over \ln(x)}dx=\ln(n+1)$
19716
What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?
101289
Studying the equation $\ln(x)- 1+ x^2=0$
7903
Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$
98344
Prove that $\int_0^1[f''(x)]^2dx\ge4.$
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
105707
A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
5229
Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$.
5034
A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$
15809
The problem of x = ln(x)
45841
integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration?
26608
How to show that $\int_{0}^{\pi}{\sin^5 x\over 1+\cos^3 x}\mathrm dx=\ln 3?$
131876
Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$
20476
Today a student asked me $\int \ln (\sin x) \, dx.$
24716
$\int_0^\infty\frac{\log x dx}{x^2-1}$ with a hint.
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
74454
Sophomore's dream: $\int_0^{1} x^{-x} \; dx = \sum_{n=1}^\infty n^{-n}$