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### Questions (160)

 109 A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$ 80 Complexity class of comparison of power towers 65 Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$ 64 Closed form for $\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx$ 62 Integral $\int_1^\infty\frac{\operatorname{arccot}\left(1+\frac{2\pi}{\operatorname{arcoth}x-\operatorname{arccsc}x}\right)}{\sqrt{x^2-1}}\mathrm dx$

### Reputation (21,683)

 +10 Integral $\int_0^\infty\frac{\tanh^2(x)}{x^2}dx$ +45 A pair of sequences defined by mutual addition/multiplication +10 Closed-form of $\int_0^1 \frac{\operatorname{Li}_2\left( x \right)}{\sqrt{1-x^2}} \,dx$ +5 Integral involving Clausen function ${\large\int}_0^{2\pi}\operatorname{Cl}_2(x)^2\,x^p\,dx$

 55 Surprising identities / equations 44 A definite integral $\int_0^\infty\frac{2-\cos x}{\left(1+x^4\right)\,\left(5-4\cos x\right)}dx$ 39 How to find $\int_0^\infty\frac{\log\left(\frac{1+x^{4+\sqrt{15}}}{1+x^{2+\sqrt{3}}}\right)}{\left(1+x^2\right)\log x}\mathrm dx$ 38 Integral $\int_0^1\frac{x^9\left(x^4+x^2-x-1-5\ln x\right)}{\left(x^{10}-1\right)\ln x}\mathrm dx$ 38 What is $(26+15(3)^{1/2})^{1/3}+(26-15(3)^{1/2})^{1/3}$?

### Tags (136)

 653 integration × 87 217 trigonometry × 24 628 closed-form × 98 207 special-functions × 60 613 calculus × 110 175 improper-integrals × 15 546 definite-integrals × 88 95 hypergeometric-function × 27 287 logarithms × 30 53 polylogarithm × 21

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