13 Solving the integral $\int_0^1\int_0^1\frac{1}{(1-\alpha x^\beta y^\gamma)^2}dxdy$ 12 Evaluate $\int_0^{\pi/4}{(4\cot x\ln\sec x-x)\ln^2\tan xdx}$ 10 Evaluating $\int_0^1\frac{x^{2/3}(1-x)^{-1/3}}{1-x+x^2}dx$ 8 When to use $y = \frac{1 + x}{1 - x}$ when evaluating definite integrals 8 Hint for solving a definite integral

### Reputation (7,095)

 +20 Evaluate $\int_0^{\pi/4}{(4\cot x\ln\sec x-x)\ln^2\tan xdx}$ +10 Is there a closed-form solution for $\sum_{n=1}^{\infty} \sum_{m=1}^{\infty} \frac{1}{nm(3n+m)}$? +5 An intriguing sum +10 Prove $\sum_{n=1}^\infty\frac{H_nH_n^{(3)}}{n^2}=\frac{227}{48}\zeta(6)-\frac32\zeta^2(3)$

### Questions (25)

 21 On the evalution of an infinite sum 15 Another interesting integral related to the Omega constant 11 How many ways to colour a $4 \times 4$ grid using four colours subject to three constraints 10 A conjectured value for $\operatorname{Re} \operatorname{Li}_4 (1 + i)$ 8 Two Euler sums each containing the reciprocal of the central binomial coefficient

### Tags (120)

 325 integration × 177 46 closed-form × 17 194 definite-integrals × 87 32 summation × 13 171 calculus × 96 30 improper-integrals × 29 57 real-analysis × 32 19 trigonometric-integrals × 7 51 sequences-and-series × 32 18 gamma-function × 9