# Table of Integrals: Solving \int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}

• EngWiPy
In summary, the conversation is about a person seeking help with a difficult integral involving Bessel functions. They ask for assistance in finding an equivalent integral in a table of integrals and are directed to post in the homework help section. The conversation also mentions the forum's guidelines for acceptable content.

#### EngWiPy

Hello,
During my derivation, I am faced with the following integral:

$$\int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}\left(2\,\alpha\,\sqrt{x^2+x}\right)\,dx$$

where A, B, and C are positive integers, $$K_{(B)}$$ is the $$B^{th}$$ order modified bessel function of the second kind. I am intending to find an equivalent integral in the table of integrals. Can anyone help me, please?

saeddawoud said:
Hello,
During my derivation, I am faced with the following integral:

$$\int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}\left(2\,\alpha\,\sqrt{x^2+x}\right)\,dx$$

where A, B, and C are positive integers, $$K_{(B)}$$ is the $$B^{th}$$ order modified bessel function of the second kind. I am intending to find an equivalent integral in the table of integrals. Can anyone help me, please?

I think this forum is for general discussions rather than homework help, you should post this in homework help section,
here
https://www.physicsforums.com/forumdisplay.php?f=152"

Last edited by a moderator:
aaryan0077 said:
I think this forum is for general discussions rather than homework help

Graduate-level homework is acceptable here. This looks like it might fit -- I certainly didn't do hairy integrals with Bessel functions as an undegrad.

CRGreathouse said:
Graduate-level homework is acceptable here. This looks like it might fit -- I certainly didn't do hairy integrals with Bessel functions as an undegrad.

Okay, whatever you say.

## What is a table of integrals?

A table of integrals is a list of mathematical formulas used to solve integrals, which are mathematical expressions that represent the area under a curve. These tables are useful for quickly solving integrals without having to derive the formula each time.

## What is the general form of the integral in the table?

The general form of the integral in the table is \int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}, where A, B, and C are constants. This formula can be used to solve integrals with different values for A, B, and C.

## What does each term in the integral represent?

The term x^A represents the variable being integrated, while (x^2+x)^{B/2} represents the function being integrated. e^{-Cx} is the exponential function, and K_{(B)} is the modified Bessel function.

## How do I use the table to solve integrals?

To use the table, you need to identify the values for A, B, and C in your integral. Then, find the corresponding formula in the table and substitute the values. You can then simplify the integral using basic algebra and solve for the final answer.

## What are some common applications of the table of integrals?

A table of integrals is often used in physics, engineering, and other fields of science to solve complex integrals that arise in mathematical models. It can also be used in statistics, economics, and other areas of mathematics.