# How Do You Integrate 1/(x^2 + 4)?

• nuclearrape66
In summary, the conversation discusses the process of integrating 1/(x^2 + 4) and the formula for solving integrals of the form 1/(x^2 + a^2). The discussion also includes tips for solving integrals and a quick response from others in the conversation.
nuclearrape66
how do i integrate 1/(x^2 +4)?

What's the derivative of arctan?

1/1+x^2

See how that might be helpful?

nuclearrape66 said:
how do i integrate 1/(x^2 +4)?

$$\int \frac{1}{x^2 +4} dx$$

$$= \int \frac{1}{x^2 +(2)^2} dx$$

try x=2tan$\theta$

hmm lemem see...1 second

nuclearrape66 said:
1/1+x^2

Exactly.. so now from your function, you take 4 common, you get:

$$\frac{1}{4}\int\frac{1}{({\frac{x}{2}})^2 + 1}dx$$

Now, if you take $\frac{x}{2} = y$.. you can solve this integral.. get a hint?

Once you have done this, it would be helpful for you to remember the formula for a general case as in $$\int\frac{1}{a^2 + x^2}dx$$

Yeah rohan's post is what I was think too..

oh i see, thanks

and quick response from everyone =)

$$\int\frac{1}{x^2+a^2}dx=\frac{1}{a}\arctan\frac{x}{a}+C$$
$$\int\frac{1}{x^2+2^2}dx=\frac{1}{2}\arctan\frac{x}{2}+C$$

fermio said:
$$\int\frac{1}{x^2+a^2}dx=\frac{1}{a}\arctan\frac{x}{a}+C$$
$$\int\frac{1}{x^2+2^2}dx=\frac{1}{2}\arctan\frac{x}{2}+C$$

No need to post the solution he all ready figured it out...

## 1. What is the purpose of integrating 1/(x^2 + 4)?

The purpose of integrating 1/(x^2 + 4) is to find the area under the curve of the function. This is a commonly used technique in calculus and is useful in solving various mathematical problems.

## 2. What is the step-by-step process for integrating 1/(x^2 + 4)?

The step-by-step process for integrating 1/(x^2 + 4) involves using substitution, partial fractions, and integration by parts. First, substitute u for x^2 + 4 and then use partial fractions to break the function into simpler parts. Finally, use integration by parts to solve for the integral.

## 3. Why is it important to use substitution when integrating 1/(x^2 + 4)?

Substitution is important when integrating 1/(x^2 + 4) because it allows us to simplify the function and make it easier to integrate. By substituting u for x^2 + 4, we can break the function into simpler parts and make the integration process more manageable.

## 4. Are there any special cases when integrating 1/(x^2 + 4)?

Yes, there are special cases when integrating 1/(x^2 + 4). If the function is being integrated over a closed interval, the limits of integration must be adjusted to account for the substitution. Additionally, if the function includes trigonometric functions, the substitution may need to be modified accordingly.

## 5. How can integrating 1/(x^2 + 4) be applied in real-world scenarios?

Integrating 1/(x^2 + 4) can be applied in real-world scenarios such as calculating the velocity of an object in motion or finding the total cost of a product over a given time period. It is also used in fields such as physics and engineering to solve various mathematical problems.

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