# How to integrate this fraction function - help

• Femme_physics
Overall, the key is to remember that the constant stays in the denominator when using power rule for integration.In summary, the conversation discusses using the power rule for integration and how to correctly handle the constant when using this rule. It is important to remember that the constant stays in the denominator and can be pulled out to make the integration easier.
Use power rule for integration.

The 2 stays in the denominator.

$${{1}\over{2x^{7}}} = {{x^{-7}\over{2}}}$$

1/(2x^7) = 1/2 x^-7, not 2x^-7

Pengwuino said:
The 2 stays in the denominator.

$${{1}\over{2x^{7}}} = {{x^{-7}\over{2}}}$$

That clears it, thanks! :)

Alternatively, you may pull out any constant from the integral
such that: $$\int \frac {dx}{2x^7} = \frac {1}{2} \int \frac {1}{x^7} dx = \frac {1}{2} \int x^{-7} dx$$
it makes the integration a bit easier.

Last edited:

## 1. How do I identify the type of fraction function I need to integrate?

To identify the type of fraction function, you need to look at the expression in the denominator. If it is a linear expression (in the form of ax + b), the fraction is a rational function. If it is a quadratic expression (in the form of ax^2 + bx + c), the fraction is an irrational function.

## 2. What is the general approach to integrating a rational function?

The general approach to integrating a rational function is to rewrite it as a sum of simpler fractions using partial fraction decomposition. Then, integrate each fraction separately and combine the results to get the final answer.

## 3. How do I handle improper fractions when integrating?

Improper fractions (where the degree of the numerator is greater than or equal to the degree of the denominator) can be handled by dividing the numerator by the denominator to get a polynomial and then integrating it using the power rule.

## 4. What are some common techniques for integrating irrational functions?

Some common techniques for integrating irrational functions include substitution (where you substitute a variable to simplify the expression), trigonometric substitution (where you use trigonometric identities to simplify the expression), and integration by parts (where you split the expression into two parts and integrate each separately).

## 5. Is there a shortcut or trick for integrating fraction functions?

Unfortunately, there is no shortcut or trick for integrating fraction functions. It requires a thorough understanding of integration techniques and practice to be able to solve these types of problems effectively.

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