# Cody

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 16 A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$ 15 A closed form for the sum $\sum_{n=1}^{\infty}\left(\frac{H_n}{n}\right)^2$ 14 Why does $\sum_{k=1}^{\infty}\dfrac{{\sin(k)}}{k}={\dfrac{\pi-1}{2}}$? 11 Closed form of $\int_0^\frac{1}{2}x^n\cot(\pi x)\,dx$ 9 Integral $\int_0^\infty \log(1-e^{-a x})\cos (bx)\, dx=\frac{a}{2b^2}-\frac{\pi}{2b}\coth \frac{\pi b}{a}$

# 6,110 Reputation

 +5 Closed form for the integral $\int_{0}^{\infty}\frac{\ln^{2}(x)\ln(1+x)}{(1-x)(x^{2}+1)}dx$ +10 Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$ +10 Proof of $\int_0^\infty \frac{x^{\alpha}dx}{1+2x\cos\beta +x^{2}}=\frac{\pi\sin (\alpha\beta)}{\sin (\alpha\pi)\sin \beta }$ +10 Need a good non-graphing calculus calculator that can derive and integrate

# 70 Questions

 29 tough integral involving $\sin(x^2)$ and $\sinh^2 (x)$ 29 Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$ 25 Show $\int_{0}^{\frac{\pi}{2}}\frac{x^{2}}{x^{2}+\ln^{2}(2\cos(x))}dx=\frac{\pi}{8}\left(1-\gamma+\ln(2\pi)\right)$ 24 Closed form for the integral $\int_{0}^{\infty}\frac{\ln^{2}(x)\ln(1+x)}{(1-x)(x^{2}+1)}dx$ 21 interesting square of log sin integral

# 31 Tags

 192 integration × 92 52 complex-analysis × 21 140 definite-integrals × 54 46 sequences-and-series × 36 113 calculus × 39 37 closed-form × 7 94 real-analysis × 21 21 summation × 6 69 improper-integrals × 20 20 contour-integration × 19

# 1 Account

 Mathematics 6,110 rep 853