New posts in Contour Integration

Inverse Laplace Transform of $e^{-\sqrt{s^2+s}}$.

Complex integral with conjugate as an exponent

Contour method to show that $\int_0^\infty\frac{x-\sin x}{x^3} \, dx=\frac\pi4$

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

Show that $\int_0^\pi\frac{2\cos(2\theta)+\cos(3\theta)}{5+4\cos(\theta)}d\theta=\frac{\pi}{8}$

Show this $\int_0^\infty \frac{t\ln(2\sinh t)}{\left(3t^2+\ln^2(2\sinh t)\right)^2}~dt=0$

How can we show that $\int_{-\infty}^{+\infty}{ke^x\pm1\over \pi^2+(e^x-x+1)^2}\cdot{(e^x+1)^2\over \pi^2+(e^x+x+1)^2}\cdot 2x \,\mathrm dx=k?$

Inequality for Distribution of points in space

$\int ^{\infty}_0 \frac{\ln x}{x^2 + 2x+ 4}dx$

Compute $\int_{0}^{\infty}\frac{x\sin 2x}{9+x^{2}} \, dx$