Integrals

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Борислав - Integrand Integrals

106 Questions

 20 How to find $\int_0^\infty \prod_{k=1}^n \frac{\sin \frac{x}{2k-1}}{\frac{x}{2k-1}}\mathrm dx$ 20 Integral $\int_{-\infty}^\infty J^3_0(x) e^{i\omega x}\mathrm dx$ 20 Integral $\int_0^\infty \log(1+x^2)\frac{\cosh{\frac{\pi x}{2}}}{\sinh^2{\frac{\pi x}{2}}}\mathrm dx=2-\frac{4}{\pi}$ 17 Integral $I:=\int_0^1 \frac{\log^2 x}{x^2-x+1}\mathrm dx=\frac{10\pi^3}{81 \sqrt 3}$ 17 How to find PV $\int_0^\infty \frac{\log \cos^2 \alpha x}{\beta^2-x^2} \, \mathrm dx=\alpha \pi$

2,988 Reputation

 +5 Integral $\int_0^{\pi/2} \theta^2 \log ^4(2\cos \theta) d\theta =\frac{33\pi^7}{4480}+\frac{3\pi}{2}\zeta^2(3)$ +15 Integral $\int_0^1 dx \frac{\ln x \ln^2(1-x)\ln(1+x)}{x}$ +5 $-4\zeta(2)-2\zeta(3)+4\zeta(2)\zeta(3)+2\zeta(5)=S$ +5 Integral $\int_0^\infty \frac{\log^2 x \cos ax}{x^n-1}dx$

 13 Convergence $I=\int_0^\infty \frac{\sin x}{x^s}dx$ 13 Evaluate $\int_0^{\pi/2}\log\cos(x)dx$ 12 Integrate $\int_{-\infty}^{\infty}\exp\left(-\frac{\pi^2t(2x+1)^2}{2c^2}\right)\cos\left(\frac{(2x+1)\pi y}{c}\right)\exp(-2\pi i kx)dx$ 12 Integrate $\int_0^1 \frac{\ln x}{\sqrt{1-x^2}}dx$. HW 11 Evaluating the integral $\int_{-1}^{1} \frac{\sin{x}}{1+x^2}dx$

51 Tags

 117 integration × 135 14 real-analysis × 79 51 calculus × 85 12 fourier-analysis × 3 50 definite-integrals × 107 10 measure-theory × 3 30 analysis × 10 10 linear-algebra × 2 18 sequences-and-series × 5 10 matrices

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