Bachelor Math student :-)

Animation I like:

Complex exponential of a grid - Desmos

Convergence of sequence - Desmos (in progress...)

Domani coloring plotter

Shortcut for me:

• Evaluated with residue theorem $$\int_{-\infty}^{+\infty} \frac{e^{ax}(1+e^x)}{1+e^{2x}}dx = \pi \frac{\sin\big(\frac{\pi}{2}a\big)+\cos\big(\frac{\pi}{2}a\big)}{\sin(\pi a)}, \ a\in (0,1)$$

• Fourier type integral $$\int_{-\infty}^{+\infty}\frac{\sin x}{1+(x-x_0)^2}dx = \pi \ e^{-1}\cdot \sin(x_0), \ \forall x_0 \in \Bbb R $$

• Sometimes is a matter of contour $$I(a) =\int_{-\infty}^{+\infty}\frac{e^{ax}}{1+e^{3x}}dx = \frac{\pi}{3}\csc\left(\frac{\pi}{3}a\right), \quad a \in (0,3)$$

• Hi! On MathSE questions are written using MathJax. Please consider editing including what's your attempt on this problem!

• $\hskip2in$ centers the image DIY.