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### Answers (228)

 11 MIT Integration Bee 2017 problem:$\int_0^{\pi/2}\frac 1 {1+\tan^{2017} x} \, dx$ : Need hints 10 Locus of centre of ellipse sliding along coordinate axes? 9 What is the coefficient of $a^8b^4c^9d^9$ in $(abc+abd+acd+bcd)^{10}$? 9 Differentiation of $\sum_{n=0}^{\infty}\frac{1}{(n+1)3^n}x^{n+1}$ 8 Find the value of the limit using Riemann sum

### Reputation (7,105)

 +10 Equation of angle bisector of two 3D straight lines +10 Locus of centre of ellipse sliding along coordinate axes? +10 Find the sum of series: $\sum_{k=0}^{n} (-1)^k \binom{n}{k} \binom{2n-k}{n}$ +10 What is the coefficient of $a^8b^4c^9d^9$ in $(abc+abd+acd+bcd)^{10}$?

### Questions (58)

 12 Binomial limit $\left(\binom{3n}{n}\binom{2n}{n}^{-1}\right)^{1/n}$ as $n\to \infty$ 9 Finding $\sum_{k=0}^{n-1}\frac{\alpha_k}{2-\alpha_k}$, where $\alpha_k$ are the $n$-th roots of unity 7 Trignometric integral : $\int \frac{dx}{\sin x + \sec x}$ 6 Integrating $\int \dfrac{1+x^2}{1+x^4}dx$ 6 Compute $\int^{\pi/2}_0 \frac{dx}{(a^2\cos^2 x + b^2 \sin ^2 x)^2}$

### Tags (122)

 95 calculus × 66 45 integration × 39 61 geometry × 41 32 sequences-and-series × 13 58 limits × 33 28 combinatorics × 16 57 trigonometry × 40 26 complex-numbers × 16 53 algebra-precalculus × 34 24 ordinary-differential-equations × 18

### Bookmarks (277)

 492 What are imaginary numbers? 234 Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ 118 Advantages of IMO students in Mathematical Research 108 Why is the derivative of a circle's area its perimeter (and similarly for spheres)? 106 Are all limits solvable without L'Hôpital Rule or Series Expansion

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