User Acyex

7 votes

2 answers

258 views

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

asked Aug 18, 2021 at 20:44

4 votes

1 answer

95 views

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

integration solution-verification

asked Jun 13, 2021 at 13:21

3 votes

0 answers

144 views

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

calculus integration solution-verification

asked Jun 16, 2021 at 21:31

3 votes

2 answers

199 views

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

integration improper-integrals

asked Jul 7, 2021 at 20:09

3 votes

2 answers

113 views

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

integration improper-integrals

asked Aug 3, 2021 at 21:10

3 votes

3 answers

46 views

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

real-analysis multivariable-calculus definite-integrals multiple-integral bounds-of-integration

asked Sep 6, 2021 at 17:36

2 votes

1 answer

128 views

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

sequences-and-series limits summation

asked Sep 7, 2021 at 12:53

2 votes

3 answers

161 views

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

integration definite-integrals improper-integrals

asked Aug 13, 2021 at 22:17

2 votes

2 answers

62 views

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

trigonometry complex-numbers proof-writing

asked Aug 30, 2021 at 0:55

2 votes

2 answers

111 views

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

definite-integrals solution-verification

asked Jul 16, 2021 at 21:19

2 votes

2 answers

140 views

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

integration solution-verification

asked Jun 11, 2021 at 19:44

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?

combinatorics

asked Jun 29, 2021 at 14:42

1 vote

1 answer

57 views

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

sequences-and-series convergence-divergence

asked Jul 11, 2021 at 18:02

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]

sequences-and-series

asked Jul 11, 2021 at 19:14

1 vote

2 answers

108 views

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

real-analysis integration sequences-and-series definite-integrals infinite-product

asked Aug 1, 2021 at 9:03

1 vote

2 answers

118 views

Limits of composite functions where the function is discontinuous

limits functions

asked Aug 22, 2021 at 19:09

1 vote

0 answers

60 views

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

sequences-and-series summation

asked Oct 3, 2021 at 17:31

1 vote

1 answer

166 views

Prove the sum to product formulas with complex numbers

trigonometry complex-numbers proof-writing

asked Aug 29, 2021 at 19:25

0 votes

1 answer

84 views

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

integration trigonometry partial-fractions

asked Sep 1, 2021 at 12:44

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]

sequences-and-series

asked Aug 18, 2021 at 17:00

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.

integration limits definite-integrals riemann-sum

asked Aug 25, 2021 at 13:00

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

integration definite-integrals riemann-sum

asked Aug 25, 2021 at 22:57

0 votes

3 answers

156 views

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

integration definite-integrals contest-math

asked Aug 3, 2021 at 12:10

0 votes

0 answers

33 views

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

sequences-and-series

asked Aug 4, 2021 at 10:56

0 votes

0 answers

34 views

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

functions proof-writing monotone-functions

asked Aug 4, 2021 at 11:52

0 votes

0 answers

125 views

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

integration definite-integrals

asked Jul 15, 2021 at 18:41

0 votes

1 answer

94 views

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

integration solution-verification

asked Jun 27, 2021 at 16:38

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27 Questions

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

Limits of composite functions where the function is discontinuous

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

Prove the sum to product formulas with complex numbers

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

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

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

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

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

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

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

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

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