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Faoler
  • Member for 1 year, 11 months
  • Last seen this week
  • Iraq
11 votes
0 answers
248 views

Solve the integral $\int_0^1 \frac{\ln^2(x+1)-\ln\left(\frac{2x}{x^2+1}\right)\ln x+\ln^2\left(\frac{x}{x+1}\right)}{x^2+1} dx$

5 votes
1 answer
236 views

How to find the coefficient of $x^k$ in the expression $\prod_{p=1}^n (x^p+1)^p$?

4 votes
1 answer
80 views

how to find expression of $a\text{ mod } n$ using polynomial of $e^{\frac{2a\pi i}{n}}$?

3 votes
1 answer
143 views

closed form for $\psi^{(-2)}\left(\frac{1}{4} \right)$

3 votes
0 answers
186 views

how to find closed form for $\int_0^1 \frac{x}{x^2+1} \left(\ln(1-x) \right)^{n-1}dx$?

3 votes
2 answers
229 views

Is there a closed form expression for $ \sum_{n=2}^\infty \frac{1}{n \sqrt{n^2-1}} $?

2 votes
1 answer
60 views

how to divide $a^{n-1} x^n+x((-1)^n+a^n)+a^{n-1}$ by $ax+1$?

2 votes
1 answer
94 views

How to evaluate $\lim\limits_{x\to 0} \frac{d}{dx} \frac{e^{-ax}-e^{-bx}}{x} $ using integral?

2 votes
3 answers
87 views

how can I solve the equation $19^x+23^y=100z$ for integers $x,y,z$?

1 vote
0 answers
132 views

how to evaluate inverse Laplace transform of $e^{- \sqrt{s}} $ using series?

1 vote
1 answer
81 views

how to deal with prime number and mod operation?

1 vote
2 answers
65 views

how to prove $\forall a_n \in \mathbb{R}, n\in \mathbb{N} \exists x \in \mathbb{R} : \sum_{k=1}^n a_k \left( x^k-\frac{1}{k+1} \right)=0 $?

1 vote
1 answer
98 views

how to evaluate $\sum_{n=1}^\infty \sum_{m=1}^{n-1} \frac{(-t)^{m+n}}{m-n}$?