user avatar
user avatar
user avatar
Acyex
  • Member for 1 year, 6 months
  • Last seen more than a month ago
7 votes
2 answers
258 views

Evaluate $\int_0^\infty \sum^{\lfloor x\rfloor}_{n=1}\frac{\sin nx\pi}{x^n}dx$

4 votes
1 answer
95 views

My solution to $\int \frac{1}{x^2\sqrt{x^2+1}}dx$

3 votes
0 answers
144 views

My solution to $\int \sqrt{\tan(x)}dx$

3 votes
2 answers
199 views

Curious and short question about $\int^\infty_0 \frac{\sin^2(x)}{x^2(x^2+1)}dx$

3 votes
2 answers
113 views

Same bounds after substitution on $\int_{-\infty}^\infty e^{-x^2-\frac{1}{x^2}}dx$ [duplicate]

3 votes
3 answers
46 views

$\iiint_M (x+y+z)\,dx\,dy\,dz$ over $M=\{(x,y,z)\in\mathbb{R^3}: 0≤z≤(x^2+y^2)^2≤81\}$

2 votes
1 answer
128 views

Evaluating $\lim_{n\to\infty}\sum_{1\leq i<k\leq n}\ln(\sqrt[n]{\frac{3n-2i}{3n+2i}})\ln(\sqrt[n]{\frac{3n-2k}{3n+2k}})$

2 votes
3 answers
161 views

My attempt $\int_0^\infty -\arcsin e^{-x}dx$

2 votes
2 answers
62 views

Proving the sum to product formula with complex numbers starting from the left hand side

2 votes
2 answers
111 views

Issues on solving $\int^\frac{\pi}{2}_0\frac{\sqrt{\sin(x)}}{\sqrt{\sin(x)}+\sqrt{\cos(x)}}\,dx$

2 votes
2 answers
140 views

My solution to $\int \frac{2x^2}{x^2+4}dx$

2 votes
2 answers
284 views

How many ways can $4$ distinguishable pieces be placed on an $8\times8$ chessboard, such that no $2$ pieces are in the same row or column?

1 vote
1 answer
57 views

Why does this method of convergence fail? $\sum^\infty_{n=3}\frac{1}{n\ln n}$

1 vote
1 answer
208 views

Find a nice form of $1+\frac23+\frac{6}{3^2}+\frac{10}{3^3}+\dots$ with sigma notation [duplicate]

1 vote
2 answers
108 views

The integral of $\int_0^\frac{π}{4} \prod^\infty_{k=0} \cos(\frac{x}{2^k})dx$

1 vote
2 answers
118 views

Limits of composite functions where the function is discontinuous

1 vote
0 answers
60 views

Evaluate $\sum_{n=0}^\infty\frac{1}{n^2+1}$ [duplicate]

1 vote
1 answer
166 views

Prove the sum to product formulas with complex numbers

0 votes
1 answer
84 views

Partial fraction on $\frac{2\cos^2(x)-1}{a^2-2a\cos(x)+1}$

0 votes
0 answers
33 views

$\sum^\infty_{k=1}\frac{(-1)^{k+1}}{k}\sum^\infty_{n=0}\frac{1}{k\cdot 2^n+5}$ [duplicate]

0 votes
1 answer
64 views

$x \lim_{n\to\infty}\sum^n_{r=1}\frac{1}{n}\ln\left(\frac{1+\frac{xr}{n}}{1+\frac{x²r²}{n²}}\right)$ into an integral.

0 votes
0 answers
37 views

$x \lim_{n\to\infty}\sum^n_{r=1}\frac{1}{n}\ln\left(\frac{1+\frac{xr}{n}}{1+\frac{x²r²}{n²}}\right)$ into an integral with a method

0 votes
3 answers
156 views

My method to $\int^1_0 \log^{2020}x dx$

0 votes
0 answers
33 views

Can we use direct comparison test with sequences with $(-1)^n$?

0 votes
0 answers
34 views

$(e^{\frac{1}{(n+1)^5}}-1)\ln(n)$ proving it's monotonically decreasing

0 votes
0 answers
125 views

Formal definition on $\int^e_1 \frac{1}{x} \, dx$

0 votes
1 answer
94 views

My solution to $\int \frac{\ln(x+1)}{x^2+1}dx$