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Tom Himler's user avatar
Tom Himler's user avatar
Tom Himler
  • Member for 7 years, 1 month
  • Last seen more than a month ago
10 votes
1 answer
804 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

9 votes
1 answer
845 views

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

9 votes
4 answers
1k views

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

8 votes
2 answers
2k views

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

8 votes
2 answers
1k views

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

6 votes
3 answers
162 views

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

6 votes
1 answer
163 views

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

6 votes
3 answers
258 views

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

6 votes
3 answers
409 views

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

6 votes
1 answer
1k views

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

5 votes
1 answer
222 views

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

5 votes
2 answers
405 views

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

5 votes
1 answer
126 views

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

5 votes
1 answer
139 views

What's the derivation of this integral formula?

5 votes
4 answers
3k views

Tricky Graph Theory Puzzle

5 votes
3 answers
436 views

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

4 votes
1 answer
333 views

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

4 votes
1 answer
130 views

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

4 votes
2 answers
502 views

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

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?

4 votes
1 answer
229 views

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

4 votes
2 answers
108 views

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

4 votes
2 answers
378 views

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

4 votes
1 answer
416 views

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

3 votes
1 answer
215 views

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

3 votes
1 answer
113 views

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

3 votes
1 answer
450 views

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

3 votes
1 answer
182 views

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

3 votes
2 answers
105 views

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

3 votes
1 answer
149 views

How would I go about solving $\sum_{j=1}^\infty\sum_{k=1}^\infty \frac{1}{j^2(j+k)^2}$?