Why Does This Integral Not Converge?

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• nikos749
In summary, an integral is a mathematical concept used in calculus to find the total accumulation of a function over a given interval. It differs from a derivative, which represents the rate of change of a function at a specific point. Integrals can be complicated due to various factors and require techniques such as substitution and integration by parts to solve. They have many real-world applications in physics, engineering, statistics, and various fields of science.
nikos749
How to solve $$\int_{-\infty}^{\infty} \frac{e^{-iax}coth[sinh[bx]]}{sinh[bx]} dx$$
mathematica gives the result ::idiv: "Integral of E^(-Iax)\ Coth[Sinh[bx]]\ Csch[bx] does not converge on {-\[Infinity],\[Infinity]}."
thanks!

Hi.
How about trying complex integral. The integrand seem to have a pole of order 2 at z=0. You may calculate residue there.

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is used to calculate the total value of a function over a given interval.

2. What makes an integral complicated?

An integral can be considered complicated if it involves complex functions or if the limits of integration are difficult to evaluate. It can also be complicated if it requires advanced techniques such as integration by parts or substitution.

3. How do you solve a complicated integral?

Solving a complicated integral requires a combination of mathematical techniques and problem-solving skills. These can include using integration rules and formulas, breaking the integral into smaller parts, and applying advanced integration techniques.

4. Why are integrals important?

Integrals are important in many fields of science and engineering, as they allow us to calculate important quantities such as area, volume, and average values. They are also used in the development of mathematical models and in solving differential equations.

5. Can integrals have real-world applications?

Yes, integrals have many real-world applications, such as calculating the work done by a force, finding the center of mass of an object, and determining the amount of medication in a patient's body over time. They are also used in physics, engineering, and economics to model and solve real-world problems.

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