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15 votes

Almost finished with integral but hit roadblock $\int_{0}^{\infty}\frac{\arctan^2(x^2)}{x^2}\,dx$

real-analysis calculus integration definite-integrals asked Jul 18, 2023 at 22:32
math.stackexchange.com

12 votes

Evaluating $\int_{0}^{1}\frac{\arctan(x)}{x^2+x+1}\,dx$

real-analysis integration solution-verification definite-integrals asked Aug 13, 2023 at 3:58
math.stackexchange.com

11 votes

Any cool ways to solve $\int_{0}^{\frac{\pi}{2}}\log(1+4\sin^2x)\,dx$

integration definite-integrals alternative-proof trigonometric-integrals golden-ratio asked Jun 24, 2023 at 18:07
math.stackexchange.com

8 votes

Evaluating $\int_{-\infty}^{\infty}\frac{\arctan(\sin^2(x))}{x^2}\,dx$. My answer: $\pi\sqrt{2(\sqrt{2}-1)}$

calculus integration definite-integrals asked Jun 11, 2023 at 20:32
math.stackexchange.com

6 votes

Any other methods for evaluating $\int_{0}^{\frac{\pi}{4}}\frac{\arctan(\cos(x))}{\cos(x)}\,dx$

real-analysis integration definite-integrals special-functions alternative-proof asked Aug 26, 2023 at 2:08
math.stackexchange.com

5 votes

Can we evaluate the generalized Ahmed integral $\int_{0}^{1}\frac{\arctan(t\sqrt{2+x^2})}{\sqrt{2+x^2}(1+x^2)}\,dx$

real-analysis calculus integration definite-integrals trigonometric-integrals asked Jul 28, 2023 at 3:48
math.stackexchange.com

5 votes

Does anyone have good logarithmic integrals? And logarithmic integral identities?

integration definite-integrals logarithms harmonic-numbers asked Jun 23, 2023 at 23:50
math.stackexchange.com

5 votes

Evaluate $\int_{-\pi/2}^{\pi/2}\frac{\arctan(\sin^2(x))}{\sin^2(x)}dx$

calculus integration definite-integrals trigonometric-integrals asked Jun 10, 2023 at 21:38
math.stackexchange.com


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