Just started Antiderivatives Help?

In summary, antiderivatives are the inverse operation of derivatives and are used to calculate the original function from its derivative. They are important in various fields and can be found using integration rules and techniques. However, not all functions have antiderivatives that can be expressed in terms of elementary functions. To check if an antiderivative is correct, one can take the derivative of the function and compare it to the original function or use graphing software to plot both functions and see if they match.
  • #1
Airp
23
0

Homework Statement


F[/B]ind the Antiderivative of: (x^3-1)/(x-1). All is known is the integration formulas (i.e. ∫sinx = -cosx+c)

Homework Equations


Integration Formulas the most complicated being ∫cscx dx= -ln(cscx+cotx)+c

The Attempt at a Solution


I tried doing (x^3/x-1) -(1/x-1), but now I'm stuck I don't really know what to do next

Thank you in advance for your time :) !
 
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  • #2
Have you tried factoring the numerator?
 
  • #3
Oh! I didn't think about it!http://picardfacepalm.com/updown.gif Thank you! I tried it and it works!
 
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Related to Just started Antiderivatives Help?

What are antiderivatives?

Antiderivatives are the inverse operation of derivatives. They are used to calculate the original function from its derivative.

Why is it important to learn about antiderivatives?

Antiderivatives are important in many areas of science and math, such as physics, engineering, and economics. They are used to solve problems involving change and accumulation.

What is the process for finding an antiderivative?

The process for finding an antiderivative involves using integration rules and techniques, such as the power rule, substitution, and integration by parts. It is also important to remember to include the constant of integration.

Can antiderivatives be calculated for any function?

In most cases, yes. However, there are some functions that do not have antiderivatives that can be written in terms of elementary functions. These are known as non-elementary functions.

How can I check if my antiderivative is correct?

You can check your antiderivative by taking the derivative of the function and seeing if it matches the original function. You can also use graphing software to plot the original function and its antiderivative and see if they match.

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