How Can U-Substitution Simplify Integrating Complex Functions?

In summary, integration with brackets is a mathematical technique used to find the area under a curve, also known as indefinite integration or antiderivatives. Brackets are used to simplify the integration process by indicating that the expression inside should be treated as a single term. To solve an integration problem with brackets, techniques such as the power rule, u-substitution, or integration by parts can be used. Integration with brackets can be applied to all types of functions, but some common mistakes to avoid include forgetting to distribute the brackets, adding the constant of integration, and correctly applying the power rule. It is also important to check for any potential discontinuities or undefined points in the function before integrating.
  • #1
dvmaz
2
0
Hi

I have tried to integrate the following equation [tex]\int(3x^{2}+4)(2x^{3}+8x)^{-4}dx[/tex]

I have tried to expand the brackets, but that would not work. Is there a way I can do this?
 
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  • #2
Try a u-substitution, like u=2x^3 + 8x. It will work.

Just to let you know, your integral is missing a dx. That dx IS required.
 
  • #3
Char. Limit said:
Try a u-substitution, like u=2x^3 + 8x. It will work.

Just to let you know, your integral is missing a dx. That dx IS required.

Thank you. It worked and I put the dx
 

FAQ: How Can U-Substitution Simplify Integrating Complex Functions?

What is integration with brackets?

Integration with brackets is a mathematical technique used to find the area under a curve. It is also known as indefinite integration or antiderivatives.

What is the purpose of using brackets in integration?

Brackets are used in integration to indicate that the expression inside should be treated as a single term. This helps to simplify the integration process and make it easier to solve.

How do you solve an integration problem with brackets?

To solve an integration problem with brackets, you can use the power rule, u-substitution, or integration by parts. First, distribute the brackets if necessary, then use one of these techniques to integrate the expression inside the brackets.

Can you integrate with brackets in all types of functions?

Yes, integration with brackets can be applied to all types of functions, including polynomials, trigonometric functions, exponential functions, and logarithmic functions.

What are some common mistakes to avoid when using integration with brackets?

Some common mistakes to avoid when using integration with brackets include forgetting to distribute the brackets, forgetting to add the constant of integration, and misapplying the power rule. It is also important to check for any potential discontinuities or undefined points in the function before integrating.

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