UserX's user avatar
UserX's user avatar
UserX's user avatar
UserX
  • Member for 9 years, 7 months
  • Last seen this week
  • Ioannina
24 votes
3 answers
2k views

Prove that a positive polynomial function can be written as the squares of two polynomial functions

10 votes
4 answers
263 views

Find all polynomials with real coefficients that satisfy $(x^2-6x+8)P(x)=(x^2+2x)P(x-2)$

10 votes
4 answers
384 views

Prove $1.43 < \int_0^1 e^{x^2}\,\mathrm{d}x < \frac{e+1}{2}$

7 votes
1 answer
93 views

Intuition behind a certain limit.

7 votes
3 answers
567 views

Closed form of $\int_0^{\frac{\pi}{3}} \log^2(\sin x) \mathrm{d}x$

6 votes
3 answers
215 views

Integer solutions to $x^x=122+231y$

6 votes
1 answer
185 views

Is $\int f=f-1\iff f(\cdot)=e^{\cdot}$ proved this way correct?

5 votes
4 answers
147 views

$\frac{1}{1+2}+\frac{1}{1+2+3}+\dots+\frac{1}{1+2+3+\dots+x}=\frac{2011}{2013}$

5 votes
2 answers
111 views

An inequality with $a_n=\int_0^1 \frac{\mathrm{d}x}{\underbrace{\sqrt{2+\sqrt{2+\dots+\sqrt{2x}}}}_{n \text { times}}}$

5 votes
2 answers
419 views

$\int_{0}^{\infty} \frac{\cos(x)}{1+x^2} dx$ and $\int_{0}^{\infty} \frac {\ln(x)}{x^2+b^2} dx$

5 votes
4 answers
430 views

General formula of repeated roots.

5 votes
1 answer
152 views

General Solution of $y'(x)+p(x)e^{r(x) y(x)}=q(x)$

4 votes
1 answer
156 views

How to integrate $\displaystyle\int e^{\frac{x^3}{3}} \mathrm{d}x$

4 votes
1 answer
54 views

$(1-t^2)\frac{\mathrm{d}^2y}{\mathrm{d}t^2}-t\frac{\mathrm{d}y}{\mathrm{d}t}+(a+2q (1- 2t^2))y=0$

4 votes
4 answers
146 views

Complex number equations

4 votes
6 answers
295 views

Proving that $\int \frac{1}{x} \mathrm dx = \ln(|x|) + C_1$

4 votes
1 answer
982 views

Difficult differential equation

3 votes
2 answers
309 views

Matrix exponentiation intuition.

3 votes
2 answers
1k views

Complex number (square) root notation.

2 votes
0 answers
48 views

Solution of $\Pi(y(x)+1)+\sin(x)=y(x)+y'(x)$

2 votes
0 answers
163 views

Integral of $\int \sin^{-1} \left (e^{\sqrt x}\right )\, \mathrm{d}x$

2 votes
2 answers
86 views

Deriving $\sum\limits_{i=1}^n \frac{1}{i^2} = \frac{π^2}{6}-ψ^{(1)}(n+1)$.

2 votes
1 answer
231 views

How to find $\int_0^1 \frac {\mathrm dx}{\left \lfloor{1-\log_2(1-x)}\right \rfloor}$

2 votes
0 answers
394 views

Important integral inequalities list.

2 votes
2 answers
823 views

Minimum volume cone.

2 votes
2 answers
1k views

$a_n=2^n+3^n+6^n-1$. Find all positive integers that are primes to all terms of the sequence.

1 vote
1 answer
764 views

Schwarzian derivative of inverse function.

1 vote
0 answers
1k views

Terence Tao's problem solution

1 vote
1 answer
112 views

Inverse laplace transform in a physics problem.

1 vote
2 answers
495 views

The image of the curve with equation $z\bar z = 2\operatorname{Im} z $ under the map $w=1/z$