# SuperAbound

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 19 Integral ${\large\int}_0^1\ln(1-x)\ln(1+x)\ln^2x\,dx$ 18 Integral ${\large\int}_0^\infty\frac{\ln x}{1+x}\sqrt{\frac{x+\sqrt{1+x^2}}{1+x^2}}\ \mathrm dx$ 15 How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$ 12 Closed-form of $\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}}{n}\Psi_3(n+1)=-\int_0^1\frac{\ln(1+x)\ln^3 x}{1-x}\,dx$ 10 Integrate $\left[\arctan\left(x\right)/x\right]^{2}$ between $-\infty$ and $+\infty$

# 3,183 Reputation

 +5 Sum of product of binomial coefficients and exponential function +10 Integral ${\large\int}_0^\infty\frac{\ln x}{1+x}\sqrt{\frac{x+\sqrt{1+x^2}}{1+x^2}}\ \mathrm dx$ +10 How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods? +10 Integral $\int_0^{\pi/2} \theta^2 \log ^4(2\cos \theta) d\theta =\frac{33\pi^7}{4480}+\frac{3\pi}{2}\zeta^2(3)$

# 8 Questions

 20 Using Fourier Series to compute sums 7 Sum $\sum^\infty_{n=1}\frac{(-1)^nH_n}{(2n+1)^2}$ 7 Integral $\int^1_0\frac{\ln{x} \ \mathrm{Li}_2(x)}{1-x}dx$ 5 Ordered partitions of an integer (with a twist) 5 Clarification of Contour Integration [duplicate]

# 57 Tags

 167 calculus × 34 56 real-analysis × 15 150 integration × 37 35 sequences-and-series × 11 120 definite-integrals × 24 30 polylogarithm × 8 74 closed-form × 7 21 trigonometry × 13 69 improper-integrals × 10 19 logarithms

# 1 Account

 Mathematics 3,183 rep 326

 Custodian × 4 Enlightened Nice Answer × 6 definite-integrals Suffrage Revival Nice Question calculus Necromancer integration

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