How to calculate [math]\int_ {0} ^ {\infty} \frac {x^ {2} *x^ {\frac {1} {3}}} {(x+1) ^ {4}} dx[/math] by the use of a keyhole contour (complex analysis, definite integrals, residue calculus, math) - Quora
![complex analysis - Calculation of the $\int_{-\infty}^{\infty} \frac{dx}{1+x^2}$ using contour integration - Mathematics Stack Exchange complex analysis - Calculation of the $\int_{-\infty}^{\infty} \frac{dx}{1+x^2}$ using contour integration - Mathematics Stack Exchange](https://i.stack.imgur.com/3McmR.jpg)
complex analysis - Calculation of the $\int_{-\infty}^{\infty} \frac{dx}{1+x^2}$ using contour integration - Mathematics Stack Exchange
![SOLVED: Definite Integration using Residue Theorem: BOAS Chapter 14,section 7, example 3 discusses the computation of the +0 cos(x) integral [ = dx using a contour lying in the upper half plane. SOLVED: Definite Integration using Residue Theorem: BOAS Chapter 14,section 7, example 3 discusses the computation of the +0 cos(x) integral [ = dx using a contour lying in the upper half plane.](https://cdn.numerade.com/ask_images/ee947b7b9175425c8256876d5e14e176.jpg)
SOLVED: Definite Integration using Residue Theorem: BOAS Chapter 14,section 7, example 3 discusses the computation of the +0 cos(x) integral [ = dx using a contour lying in the upper half plane.
![ordinary differential equations - Where is the contour integration indicated? - Mathematics Stack Exchange ordinary differential equations - Where is the contour integration indicated? - Mathematics Stack Exchange](https://i.stack.imgur.com/kEzEp.png)