Newbetuts

Computation of $\int_{-\infty}^{\infty} \left(\frac{\sin x}{x}\right)^2e^{itx}dx$ for real $t$ [duplicate]

Hard! Integrate $\int_0^{\frac{\pi}{2}}\frac{x\ln|\cot (x-\frac{\pi}{4})|}{\sin^2x}{d}x=\frac{\pi^{2}}{4}+\frac{\pi}{2}\ln2$

Solve $\int _{x=0}^{\infty }\int _{t=-\infty }^{\infty }\exp \left(\frac{-a t^2+i b t}{3 t^2+1}+i t x\right)\frac{x}{3 t^2+1}\mathrm{d}t\mathrm{d}x$

Why do we use only upper half plane to do Residue Integration?

Integrate $\int_0^\infty \frac{dx}{(x^2+2x+12)^2}$ using residues

Why do we need to worry about removable singularities when using Residue Theorem?

Residues and poles proof

Conjectured value of a difficult integral with Dedekind eta functions

Is there a rapider or more elegant way to evaluate $\int_0^{+\infty} \frac{\cos(\pi x)\ \text{d}x}{e^{2\pi \sqrt{x}}-1}$?

Applications of Residue Theorem in complex analysis?

finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis

Evaluate $\int_{0}^{\infty}\dfrac{\mathrm dx}{(e^{\pi x}+e^{-\pi x})(16+x^2)}$

Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory

Using residue theorem to calculate following integral

Why is the (-1)-th coefficient of $f^n f'$ equal to 0, without dividing by $n+1$?

New posts in residue-calculus

Computation of $\int_{-\infty}^{\infty} \left(\frac{\sin x}{x}\right)^2e^{itx}dx$ for real $t$ [duplicate]

Partial fraction expansion for non-rational functions

Calculate Integral using residue theorem

Application of the residue theorem

$\int_0^\infty \frac{1}{1+x^ 9} \, dx$

Integrating around simple pole and semicircle

Hard! Integrate $\int_0^{\frac{\pi}{2}}\frac{x\ln|\cot (x-\frac{\pi}{4})|}{\sin^2x}{d}x=\frac{\pi^{2}}{4}+\frac{\pi}{2}\ln2$

Solve $\int _{x=0}^{\infty }\int _{t=-\infty }^{\infty }\exp \left(\frac{-a t^2+i b t}{3 t^2+1}+i t x\right)\frac{x}{3 t^2+1}\mathrm{d}t\mathrm{d}x$

Why do we use only upper half plane to do Residue Integration?

Integrate $\int_0^\infty \frac{dx}{(x^2+2x+12)^2}$ using residues

Why do we need to worry about removable singularities when using Residue Theorem?

Residues and poles proof

Conjectured value of a difficult integral with Dedekind eta functions

Is there a rapider or more elegant way to evaluate $\int_0^{+\infty} \frac{\cos(\pi x)\ \text{d}x}{e^{2\pi \sqrt{x}}-1}$?

Applications of Residue Theorem in complex analysis?

finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis

Evaluate $\int_{0}^{\infty}\dfrac{\mathrm dx}{(e^{\pi x}+e^{-\pi x})(16+x^2)}$

Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory

Using residue theorem to calculate following integral

Why is the (-1)-th coefficient of $f^n f'$ equal to 0, without dividing by $n+1$?