How do I integrate (x^2+a^2)^(-3/2)?

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In summary, an integral is a mathematical concept that represents the area under a curve on a graph. The process of solving an integral involves finding the antiderivative of a function and evaluating it at specific limits. There are several types of integrals, each with its own rules and applications. Solving integrals is important because it allows us to find solutions to various problems and is a fundamental concept in calculus. There are several techniques for solving integrals, such as substitution, integration by parts, trigonometric substitution, and partial fractions. These techniques are used to simplify the integral and make it easier to solve.
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I haven't done basic integrals for awhile...but just wondering how you would integrate the following functions without looking it up in the integral table.

(x^2+a^2)^(-3/2) where a is a constant.

Thanks!
 
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Make the substitution [itex] x=a\sinh t [/itex] and then see what you get.
 
  • #3
The substitution [itex]x= atan(\theta)[/itex] will also work.
 

FAQ: How do I integrate (x^2+a^2)^(-3/2)?

What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to solve a variety of problems in mathematics, physics, and other fields.

What is the process of solving an integral?

The process of solving an integral involves finding the antiderivative of a function and then evaluating it at specific limits. This process is also known as integration.

What are the different types of integrals?

There are several types of integrals, including definite integrals, indefinite integrals, improper integrals, and multiple integrals. Each type has its own rules and applications.

Why is solving integrals important?

Solving integrals is important because it allows us to find solutions to various problems in mathematics and other fields. It is also a fundamental concept in calculus and is used in many real-life applications.

What are some common techniques for solving integrals?

There are several techniques for solving integrals, including substitution, integration by parts, trigonometric substitution, and partial fractions. These techniques are used to simplify the integral and make it easier to solve.

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