User Tom Himler

10 votes

1 answer

771 views

Show $\int_0^{2\pi} \exp\left(\frac{7+5 \cos x}{10+6\cos x}\right) \cos \left( \frac{\sin x}{10+6 \cos x} \right) dx = 2\pi e^{2/3}$ Real Methods

asked Sep 10, 2018 at 2:13

9 votes

1 answer

790 views

Evaluate $\sum_{n=1}^\infty \arctan\left(\frac{1}{8n^2} \right)$

asked Jan 6, 2019 at 18:14

8 votes

2 answers

1k views

Solve $ \int_0^2 \sqrt{x+\sqrt{x+\sqrt{x+\dotsb}}}\,dx $

asked Sep 1, 2017 at 2:41

8 votes

2 answers

2k views

What is the 3rd Derivative of Cos(x) using this Derivative Formula?

asked Oct 16, 2017 at 18:28

8 votes

4 answers

692 views

How do you Evaluate $\int_{-\infty}^\infty \frac{\cos(x)}{x^2+1}dx$ Without Using Residue Calculus

asked Nov 5, 2017 at 0:40

6 votes

3 answers

159 views

Closed form $\sum_{n=0}^\infty \frac{\cos(n)}{(2n+1)(2n+2)} $

asked Mar 12, 2018 at 15:11

6 votes

1 answer

146 views

Evaluate $\int_0^1 \frac{1}{1+x^m}dx$ for $m>0 $

asked Jul 18, 2018 at 3:05

6 votes

3 answers

249 views

Evaluate $\sum_{n=0}^\infty (-1)^n \ln\frac{2+2n}{1+2n}$

asked Aug 14, 2018 at 18:06

6 votes

3 answers

373 views

Evaluate $\int_0^1 \frac{\operatorname{arctanh}^3(x)}{x}dx$

asked Dec 30, 2018 at 17:24

6 votes

1 answer

733 views

Evaluate $\sum_{n=2}^\infty \frac{\ln(n)(-1)^n}{n^2} $

asked Jan 4, 2019 at 15:18

5 votes

1 answer

213 views

Evaluate $\int_{0}^\frac{\pi}{2} \sqrt{1+\sin^2(x)}dx$

asked Jul 7, 2019 at 19:42

5 votes

1 answer

122 views

Evaluate $\int_0^\infty \cos(bx)(x-\ln(e^x-1))dx $

asked Aug 7, 2018 at 18:34

5 votes

1 answer

136 views

What's the derivation of this integral formula?

asked Oct 31, 2017 at 4:01

5 votes

4 answers

3k views

Tricky Graph Theory Puzzle

asked Apr 10, 2018 at 18:09

5 votes

2 answers

390 views

Why does $\sum_{n=0}^\infty \frac{n!}{(2n+1)!!}$ converge to $\frac{\pi}{2}$

asked Nov 11, 2017 at 0:20

4 votes

1 answer

300 views

Evaluate $\int_{0}^{\frac{\pi}{2}} \sinh^{-1}(\sin(x))dx$

asked Nov 14, 2017 at 0:08

4 votes

1 answer

124 views

Evaluate $\int_{0}^{\infty}e^{-x^2}\ln(x)dx$

asked Nov 28, 2017 at 20:24

4 votes

2 answers

457 views

Evaluate $\int_{0}^\infty \sin\left(\frac{1}{x}\right)\sin\left(x^2\right)\,dx$

asked Jan 3, 2018 at 4:05

4 votes

2 answers

92 views

Why is $\int_0^\infty f(x) \, dx = \frac{1}{2}\int_0^\infty f(x) \,dx+ \frac{f(\frac{1}{x})}{x^2} \, dx $ true?

asked Nov 9, 2017 at 0:29

4 votes

1 answer

210 views

Evaluate $\int_{-\infty}^\infty e^{x/2}\operatorname{sech}(x)\,dx$ without Residue Calculus

asked Jun 25, 2018 at 15:35

4 votes

2 answers

103 views

General formula for Evaluating $\sum_{n=0}^\infty n^ar^n$ where $ |r|<1 , a\ge0$

asked Feb 8, 2018 at 20:46

4 votes

2 answers

356 views

Evaluate $\int_{0}^{\frac{\pi}{2}} x\ln(\tan(x))dx $ [duplicate]

asked Dec 24, 2018 at 0:49

4 votes

1 answer

379 views

Integral $\int_{0}^\frac{\pi}{2} \ln(1+a\sin x)\csc(x)dx $

asked Jun 15, 2019 at 1:42

4 votes

2 answers

385 views

Integrate $\int_{0}^\infty \frac{\tanh(x)}{x^3}-\frac{\operatorname{sech}(x)}{x^2}dx$

asked Sep 4, 2019 at 19:43

3 votes

1 answer

170 views

Closed form for $\int_{0}^1 \frac{\ln(x)\ln(1-x)^b}{x^2}dx$

asked Nov 1, 2019 at 1:18

3 votes

1 answer

204 views

Show that $\int_{0}^\infty \frac{1}{(1+x-u)(\pi^2+\ln^2(x))}dx=\frac{1}{u}+\frac{1}{\ln(1-u)}$

asked Jun 24, 2019 at 3:40

3 votes

1 answer

106 views

Closed form for $\int_{0}^1 \frac{u\ln(2)-\ln(1+u)}{\ln(u)u}du$

asked Dec 17, 2018 at 23:17

3 votes

1 answer

436 views

Using the Harmonic Addition Theorem to simplify $\cos(x)+i\sin(x)$

asked Sep 5, 2018 at 23:03

3 votes

1 answer

175 views

Is there another way of evaluating $\lim_{x \to 0} \Gamma(x)(\gamma+\psi(1+x))=\frac{\pi^2}{6}$

asked Aug 2, 2018 at 14:43

3 votes

2 answers

104 views

Why does $\int_{-\pi}^{\pi}\ln(a^2+e^2+2ea\cos(\theta))d\theta = 4\pi$ only for $-e\leq a\leq e$

asked Sep 15, 2018 at 1:33

Stack Exchange Network

61 Questions

Show $\int_0^{2\pi} \exp\left(\frac{7+5 \cos x}{10+6\cos x}\right) \cos \left( \frac{\sin x}{10+6 \cos x} \right) dx = 2\pi e^{2/3}$ Real Methods

Evaluate $\sum_{n=1}^\infty \arctan\left(\frac{1}{8n^2} \right)$

Solve $ \int_0^2 \sqrt{x+\sqrt{x+\sqrt{x+\dotsb}}}\,dx $

What is the 3rd Derivative of Cos(x) using this Derivative Formula?

How do you Evaluate $\int_{-\infty}^\infty \frac{\cos(x)}{x^2+1}dx$ Without Using Residue Calculus

Closed form $\sum_{n=0}^\infty \frac{\cos(n)}{(2n+1)(2n+2)} $

Evaluate $\int_0^1 \frac{1}{1+x^m}dx$ for $m>0 $

Evaluate $\sum_{n=0}^\infty (-1)^n \ln\frac{2+2n}{1+2n}$

Evaluate $\int_0^1 \frac{\operatorname{arctanh}^3(x)}{x}dx$

Evaluate $\sum_{n=2}^\infty \frac{\ln(n)(-1)^n}{n^2} $

Evaluate $\int_{0}^\frac{\pi}{2} \sqrt{1+\sin^2(x)}dx$

Evaluate $\int_0^\infty \cos(bx)(x-\ln(e^x-1))dx $

What's the derivation of this integral formula?

Tricky Graph Theory Puzzle

Why does $\sum_{n=0}^\infty \frac{n!}{(2n+1)!!}$ converge to $\frac{\pi}{2}$

Evaluate $\int_{0}^{\frac{\pi}{2}} \sinh^{-1}(\sin(x))dx$

Evaluate $\int_{0}^{\infty}e^{-x^2}\ln(x)dx$

Evaluate $\int_{0}^\infty \sin\left(\frac{1}{x}\right)\sin\left(x^2\right)\,dx$

Why is $\int_0^\infty f(x) \, dx = \frac{1}{2}\int_0^\infty f(x) \,dx+ \frac{f(\frac{1}{x})}{x^2} \, dx $ true?

Evaluate $\int_{-\infty}^\infty e^{x/2}\operatorname{sech}(x)\,dx$ without Residue Calculus

General formula for Evaluating $\sum_{n=0}^\infty n^ar^n$ where $ |r|<1 , a\ge0$

Evaluate $\int_{0}^{\frac{\pi}{2}} x\ln(\tan(x))dx $ [duplicate]

Integral $\int_{0}^\frac{\pi}{2} \ln(1+a\sin x)\csc(x)dx $

Integrate $\int_{0}^\infty \frac{\tanh(x)}{x^3}-\frac{\operatorname{sech}(x)}{x^2}dx$

Closed form for $\int_{0}^1 \frac{\ln(x)\ln(1-x)^b}{x^2}dx$

Show that $\int_{0}^\infty \frac{1}{(1+x-u)(\pi^2+\ln^2(x))}dx=\frac{1}{u}+\frac{1}{\ln(1-u)}$

Closed form for $\int_{0}^1 \frac{u\ln(2)-\ln(1+u)}{\ln(u)u}du$

Using the Harmonic Addition Theorem to simplify $\cos(x)+i\sin(x)$

Is there another way of evaluating $\lim_{x \to 0} \Gamma(x)(\gamma+\psi(1+x))=\frac{\pi^2}{6}$

Why does $\int_{-\pi}^{\pi}\ln(a^2+e^2+2ea\cos(\theta))d\theta = 4\pi$ only for $-e\leq a\leq e$