Aryabhata

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Don't have much time these days...


870 Answers

newest activity votes
69
Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$?
41
How do I integrate the following? $\int{\frac{(1+x^{2})\mathrm dx}{(1-x^{2})\sqrt{1+x^{4}}}}$
40
Root Calculation by Hand
39
Are there integer solutions to $9^x - 8^y = 1$?
36
Which one result in maths has surprised you the most?
30
$x^y = y^x$ for integers $x$ and $y$
28
Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer?
26
Limit of the nested radical $\sqrt{7+\sqrt{7+\sqrt{7+\cdots}}}$
25
Calculating the integral $\int_{0}^{\infty} \frac{\cos x}{1+x^2}\mathrm{d}x$ without using complex analysis
25
Ways to evaluate $\int \sec \theta \, d \theta$
25
$\int \cos^2 x$ - Where did I go wrong?
25
Is there a function with a removable discontinuity at every point?
24
Prove: $\frac{n^5}5 + \frac{n^4}2 + \frac{n^3}3 - \frac n {30}$ is an integer for $n \ge 0$
24
How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$
22
Why is the area under a curve the integral?
22
What's the nth integral of $\frac1{x}$?
21
Simpler way to compute a definite integral without resorting to partial fractions?
21
Why is Pi equal to 3.14159…?
21
Is this definite integral really independent of a parameter? How can it be shown?
21
Irrationality of powers of $\pi$
20
German sofa primes: Can both $q$ and $\frac{q^3+1}{2}$ be prime?
19
$ \lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite
19
Beautiful identity: $\sum_{k=m}^n (-1)^{k-m} \binom{k}{m} \binom{n}{k} = \delta_{mn}$
19
Taking Seats on a Plane
18
Is a transcendental number necessarily irrational?
18
Is it possible to get arbitrarily near any acute angle with Pythagorean triangles?
18
Why Doesn't This Series Converge?
18
How closely can we estimate $\sum_{i=0}^n \sqrt{i}$
17
Prove $(\dfrac{2}{5})^{\frac{2}{5}}<\ln{2}$
17
Are there any $n$ for which $ n^4+n^3+n^2+n+1$ is a perfect square?
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