13 Solving the integral $\int_0^1\int_0^1\frac{1}{(1-\alpha x^\beta y^\gamma)^2}dxdy$ 9 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 7 What is the correct symbol for “equal-rounded”?

### Reputation (6,315)

 +10 Calculating the summation$\sum_{n=1}^{\infty}\frac{H_{n+1}}{n(n+1)}$ -2 How to show that $\sum_{n=1}^{\infty}\frac{H_n}{n^2+n}=\frac{\pi^2}{6}$ +10 Seeking Methods to solve $\int_{0}^{\infty} \frac{e^{-x^n}}{x^n + 1}\:dx$ +15 Evaluating what looks like a Frullani integral

### Questions (21)

 20 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 8 Two Euler sums each containing the reciprocal of the central binomial coefficient 6 On the evaluation of $\int_0^\infty e^{-x^2} \sin \left (\frac{1}{4x^2} \right ) \, dx$

### Tags (118)

 281 integration × 162 29 closed-form × 9 165 definite-integrals × 77 27 summation × 12 144 calculus × 89 25 improper-integrals × 26 49 real-analysis × 27 17 indefinite-integrals × 13 44 sequences-and-series × 24 17 algebra-precalculus × 8

### Accounts (3)

 Mathematics 6,315 rep 2829 Physics 178 rep 27 TeX - LaTeX 165 rep 16