Calculating the Antiderivative of (-4x)/(x^2 + 3) dx

In summary: If all else fails, you can always resort to simple substitution and see how that turns out.In summary, the question is asking for the antiderivative of (-4x)/(x^2 + 3) dx. One person suggests using a special technique for integrating f'/f, while another suggests trying simple substitution. Both advise showing work to receive help.
  • #1
rayray19
17
0

Homework Statement




the antiderivative of (-4x)/(x^2 + 3) dx





Homework Equations





The Attempt at a Solution



i got -2+c is that right at all, if not can somebody help me
 
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  • #2
If your answer is:

-2 + c

Then no, not even in the ballpark.

Please explain what you did to arrive there.

Note "antiderivative" is the same as "indefinite integral".

To check your answer, take the derivative. If you arrive at the question, you have the right answer.

(Unless of course you had a definite integral, in which case -2 + c could be correct after evaluating the integral on its parameters.)
 
  • #3
Here's a hint to get you going:

There's a special technique of integration if you want to find integral of f'(x)/f(x). Note that you can easily express the integral in that form.
 
  • #4
rayray; please note that you must start showing some work here in order for us to help you. Simply quoting an answer does not show what effort you have made, or even what you have done to get your answer. In this question for example, I have no idea what you have done to get your answer; but if you showed your work, I would probably be able to point out your mistakes.

As for the actual approach; I would take Defennnder's advice and try to recall how to integrate f'/f.
 

1. What is the process for calculating the antiderivative of (-4x)/(x^2 + 3) dx?

The process for calculating the antiderivative of (-4x)/(x^2 + 3) dx is to first rewrite the expression as (-4x)(x^2 + 3)^-1 and then use the power rule of integration to solve for the antiderivative.

2. Can the antiderivative of (-4x)/(x^2 + 3) dx be simplified further?

Yes, the antiderivative of (-4x)/(x^2 + 3) dx can be simplified further by using the substitution method or partial fractions, depending on the complexity of the expression.

3. What is the final answer for the antiderivative of (-4x)/(x^2 + 3) dx?

The final answer for the antiderivative of (-4x)/(x^2 + 3) dx is (-2ln(x^2 + 3)) + C, where C is the constant of integration.

4. Can the antiderivative of (-4x)/(x^2 + 3) dx be used to find the area under the curve?

Yes, the antiderivative of (-4x)/(x^2 + 3) dx can be used to find the area under the curve by evaluating the antiderivative at the given limits and taking the difference between the two values.

5. Are there any special cases to consider when calculating the antiderivative of (-4x)/(x^2 + 3) dx?

No, there are no special cases to consider when calculating the antiderivative of (-4x)/(x^2 + 3) dx. However, it is important to be careful with the signs and remember to include the constant of integration in the final answer.

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