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Accelerator
  • Member for 1 year, 10 months
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18 votes
5 answers
831 views

Integral: $\int_{0}^{2\pi}\arctan\left(\frac{1+2\cos x}{\sqrt{3}}\right)dx$

9 votes
6 answers
834 views

Integral: $\int_{0}^{1}\frac{\arctan^{2}\left(x\right)}{x}dx$

8 votes
2 answers
283 views

Evaluating $\int_{-\infty}^{\infty}\frac{\ln\left(1+x^{8}\right)}{x^{2}\left(1+x^{2}\right)^{2}}dx$

7 votes
3 answers
289 views

Evaluating $\int_{-\infty}^{\infty}\frac{\ln\left(\frac{1}{2}+x+x^{2}\right)}{1+x^{2}}dx$

6 votes
4 answers
446 views

Integral Involving Harmonic Numbers: $\int_{\sqrt{3}}^{\infty}\frac{\ln\left(x^{4}-1\right)}{x^{2}-1}dx$

6 votes
1 answer
252 views

Strange Result in Contour Integration: Possible Mistake?

5 votes
2 answers
241 views

Proof Verification: $\int_{-1}^{1}\frac{\ln{(x+1)}}{x}dx = \frac{\pi^2}{4}$

3 votes
1 answer
189 views

Proof verification: $\int_{-\infty}^{\infty}\operatorname{sech}\left(x\right)\ln\left(\cosh\left(x\right)\right)dx\ =\ \pi\ln\left(2\right)$.

2 votes
1 answer
158 views

Possible Mistake in Evaluating $\operatorname{P.V.}\int_{0}^{\pi}\tan\left(x\right)\ln\left(\cos^{2}\left(x\right)\right)dx$

2 votes
1 answer
276 views

Contour Integral Involving $e^z$, a Semicircle, and Triangle Inequality

2 votes
1 answer
298 views

Wrong Change of Variable for Improper Integral?

2 votes
0 answers
111 views

Evaluating $\int e^{ax}\cosh\left(bx\right)dx$ and $\int e^{ax}\sinh\left(bx\right)dx$ Simultaneously Using Linear Algebra

1 vote
1 answer
101 views

Proof Verification: $\int_0^{2\pi}|\sin{((n-1)x)}|dx = 4$.

1 vote
1 answer
101 views

Evaluate $\int_{0}^{\infty}x^{a}e^{-x^{3}}dx$ using spherical coordinates

0 votes
1 answer
310 views

Integral: $\int_{0}^{2\pi}\left|\sin\left(\left(n-1\right)x-\frac{\pi}{2n}\right)\cos\left(nx\right)\right|dx$

0 votes
2 answers
132 views

Is $\left|\frac{\tanh^{2}\left(z\right)}{z^{2}}\right|\le\frac{1}{\left|z\right|^{2}}$?