| 562694 | Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$ | proof verified | Read PDF TeX |
| 712798 | Crazy $\int_0^\infty{_3F_2}\left(\begin{array}c\tfrac58,\tfrac58,\tfrac98\\\tfrac12,\tfrac{13}8\end{array}\middle|\ {-x}\right)^2\frac{dx}{\sqrt x}$ | proof verified | Read PDF TeX |
| 908108 | How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$ | proof verified | Read PDF TeX |
| 1142705 | Evaluate $\int_0^{\pi/2}\frac{x^2\log^2{(\sin{x})}}{\sin^2x}dx$ | proof verified | Read PDF TeX |
| 1595389 | Integral ${\large\int}_0^{\pi/2}\arctan^2\!\left(\frac{\sin x}{\sqrt3+\cos x}\right)dx$ | proof equivalent | Read PDF TeX |
| 1588996 | Yet another log-sin integral $\int\limits_0^{\pi/3}\log(1+\sin x)\log(1-\sin x)\,dx$ | proof verified | Read PDF TeX |
| 418134 | Calculating $\int_{\pi/2}^{\pi}\frac{x\sin{x}}{5-4\cos{x}}\,\mathrm dx$ | proof verified | Read PDF TeX Lean |
| 1279165 | Integrals of the form ${\large\int}_0^\infty\operatorname{arccot}(x)\cdot\operatorname{arccot}(a\,x)\cdot\operatorname{arccot}(b\,x)\ dx$ | proof equivalent | Read PDF TeX |
| 905653 | How to find ${\large\int}_1^\infty\frac{1-x+\ln x}{x \left(1+x^2\right) \ln^2 x} \mathrm dx$? | proof verified | Read PDF TeX |
| 714628 | Closed form for $\int_{-\infty}^0\operatorname{Ei}^3x\,dx$ | proof verified | Read PDF TeX |
| 918680 | Closed Form for the Imaginary Part of $\text{Li}_3\Big(\frac{1+i}2\Big)$ | proof equivalent | Read PDF TeX |
| 918821 | Closed form for ${\large\int}_0^1\frac{\ln^2x}{\sqrt{1-x+x^2}}dx$ | proof equivalent | Read PDF TeX |
| 1150822 | Closed form for $\int_0^\infty\arctan\Bigl(\frac{2\pi}{x-\ln\,x+\ln(\frac\pi2)}\Bigr)\frac{dx}{x+1}$ | proof verified | Read PDF TeX |
| 1376159 | A difficult logarithmic integral ${\Large\int}_0^1\log(x)\,\log(2+x)\,\log(1+x)\,\log\left(1+x^{-1}\right)dx$ | proof incomplete | Read PDF TeX |
| 970125 | Evaluate $\int_0^1\frac{\ln(1-x)}{x}\text{Li}_3\left(\frac{1+x}{2}\right)dx$ , $\int_0^1\frac{\ln^2(1-x)}{x}\text{Li}_2\left(\frac{1+x}{2} \right)dx$ | proof verified | Read PDF TeX |
| 1372767 | Integral $\int_0^1\frac{\log(x)\log(1+x)}{\sqrt{1-x}}\,dx$ | proof equivalent | Read PDF TeX |
| 1153708 | Closer form for $\int_0^\infty\frac{(\arctan{x})^2\log^2({1+x^2})}{x^2}dx$ | proof verified | Read PDF TeX |
| 570997 | Integral $\int_0^1\frac{\ln\left(x+\sqrt2\right)}{\sqrt{2-x}\,\sqrt{1-x}\,\sqrt{\vphantom{1}x}}\mathrm dx$ | proof verified | Read PDF TeX |
| 909228 | Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^32^n}$ | proof verified | Read PDF TeX |
| 1550806 | Closed form solution to $\int_0^1\arctan^2(x)\,\sqrt{x}\,dx$ | proof equivalent | Read PDF TeX |
| 564816 | Integral $\int_0^{\pi/2}\arctan^2\left(\frac{6\sin x}{3+\cos 2x}\right)\mathrm dx$ | proof verified | Read PDF TeX |
| 577849 | Derivative of the Meijer G-function with respect to one of its parameters | proof verified | Read PDF TeX |
| 557439 | Integral $\int_0^\infty\frac{\operatorname{arccot}\left(\sqrt{x}-2\,\sqrt{x+1}\right)}{x+1}\mathrm dx$ | proof verified | Read PDF TeX |
| 554624 | Integral $\int_0^\infty\frac{1}{x\,\sqrt{2}+\sqrt{2\,x^2+1}}\cdot\frac{\log x}{\sqrt{x^2+1}}\mathrm dx$ | not attempted | — |
| 927427 | Does $\int_0^1\frac{\ln x}{1+x}\cos^{-1}x\,\mathrm dx$ have a closed from? | not attempted | — |
| 577704 | Integral $\int_0^\infty\frac{\ln\left(1+x+\sqrt{x^2+2\,x}\right)\,\ln\left(1+\sqrt{x^2+2\,x+2}\right)}{x^2+2x+1}dx$ | not attempted | — |
| 578605 | Integral $\int_0^\infty\frac{\ln\left(\sqrt{x+1\vphantom{x^0}}-1\right)\,\ln\left(\sqrt{x^{-1}+1}+1\right)}{(x+1)^{3/2}}dx$ | not attempted | — |
| 702681 | Integral $\int_0^1\frac{\log(1-x)}{\sqrt{x-x^3}}dx$ | not attempted | — |
| 935366 | Simplification of an expression containing $\operatorname{Li}_3(x)$ terms | not attempted | — |
| 967398 | Extract real and imaginary parts of $\operatorname{Li}_2\left(i\left(2\pm\sqrt3\right)\right)$ | not attempted | — |
| 930011 | Closed-forms for several tough integrals | not attempted | — |
| 964438 | Integral $\int_0^1\frac{x^{42}}{\sqrt{x^4-x^2+1}}\operatorname d \!x$ | not attempted | — |
| 572859 | Closed form for $\int_0^\infty\frac{\sin x\,\cdot\,\operatorname{Ci}x-\cos x\,\cdot\,\operatorname{Si}x}{\sqrt{16\,x^2+1}}dx$ | not attempted | — |
| 581215 | Integral $\int_0^\infty x^2\,e^{-x^2}\operatorname{erf}(x)\,\log(x)\,dx$ | not attempted | — |
| 904320 | Improper integral containing $\sqrt{\cos x-\frac1{\sqrt 2}}$ in the denominator | not attempted | — |
| 710175 | Integral $\int_0^1\frac{\ln x}{x-1}\ln\left(1+\frac1{\ln^2x}\right)dx$ | not attempted | — |
| 576304 | A closed form for $\int_0^1{_2F_1}\left(-\frac{1}{4},\frac{5}{4};\,1;\,\frac{x}{2}\right)^2dx$ | not attempted | — |
| 704917 | Integral $\int_0^\infty F(x)\,F\left(x\,\sqrt2\right)\frac{e^{-x^2}}{x^2} \, dx$ involving Dawson's function | not attempted | — |
| 566513 | Closed form for $\int_0^1\sqrt{\frac{2-x}{(1-x)\,x}}\,\log\left(\frac{(2-x)\,x}{1-x}\right)dx$ | not attempted | — |