Ryan
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### Questions (54)

 48 Show that $\int_{0}^{\pi/2}\frac {\log^2\sin x\log^2\cos x}{\cos x\sin x}\mathrm{d}x=\frac14\left( 2\zeta (5)-\zeta(2)\zeta (3)\right)$ 18 A log improper integral 18 A series involves harmonic number 17 Find the infinite sum $\sum_{n=1}^{\infty}\frac{1}{2^n-1}$ 16 How to evaluate $\int_{0}^{1}{\frac{{{\ln }^{2}}\left( 1-x \right){{\ln }^{2}}\left( 1+x \right)}{1+x}dx}$

### Reputation (1,538)

 +10 Show that $\int_{0}^{\pi/2}\frac {\log^2\sin x\log^2\cos x}{\cos x\sin x}\mathrm{d}x=\frac14\left( 2\zeta (5)-\zeta(2)\zeta (3)\right)$ +5 Definite integral, quotient of logarithm and polynomial +5 Evaluate $\int_{0}^{+\infty }{\left( \frac{x}{{{\text{e}}^{x}}-{{\text{e}}^{-x}}}-\frac{1}{2} \right)\frac{1}{{{x}^{2}}}\text{d}x}$ +5 A improper integral with Glaisher-Kinkelin constant

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### Tags (31)

 0 calculus × 46 0 fourier-analysis × 10 0 integration × 42 0 fourier-series × 7 0 real-analysis × 34 0 limits × 6 0 sequences-and-series × 34 0 summation × 5 0 improper-integrals × 11 0 riemann-zeta × 4

### Account (1)

 Mathematics 1,538 rep 619