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Mathematics
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15
Almost finished with integral but hit roadblock $\int_{0}^{\infty}\frac{\arctan^2(x^2)}{x^2}\,dx$
Jul 18, 2023
12
Evaluating $\int_{0}^{1}\frac{\arctan(x)}{x^2+x+1}\,dx$
Aug 13, 2023
11
Any cool ways to solve $\int_{0}^{\frac{\pi}{2}}\log(1+4\sin^2x)\,dx$
Jun 24, 2023
8
Evaluating $\int_{-\infty}^{\infty}\frac{\arctan(\sin^2(x))}{x^2}\,dx$. My answer: $\pi\sqrt{2(\sqrt{2}-1)}$
Jun 11, 2023
6
Any other methods for evaluating $\int_{0}^{\frac{\pi}{4}}\frac{\arctan(\cos(x))}{\cos(x)}\,dx$
Aug 26, 2023
5
Evaluate $\int_{-\pi/2}^{\pi/2}\frac{\arctan(\sin^2(x))}{\sin^2(x)}dx$
Jun 10, 2023
5
Does anyone have good logarithmic integrals? And logarithmic integral identities?
Jun 23, 2023
4
Evaluating $\int_{0}^{\infty}\frac{\sin^2(x)}{x^2(1+x^2)}\,dx$
Jun 21, 2023
4
Generalized log integral $\int_{0}^{\frac{\pi}{2}}\log(a+\sin(x))\,dx$
Jul 29, 2023
3
Conjecture about the value of $\int_{-\infty}^{\infty}\frac{e^{\cos(x)}\sin(\sin(x))}{x}\,dx$
Jul 20, 2023