Anti Derivative of 20/(1+x^(2))

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In summary, the formula for the anti derivative of 20/(1+x^(2)) is 20 tan^-1(x) + C, where C is the constant of integration. To solve for the anti derivative, you can use this formula or integration by substitution or parts. The constant of integration, represented by C, is used to account for any possible lost values of the original function. The anti derivative can be simplified to 20 tan^-1(x) + C, but the constant of integration must be included. The graph of the anti derivative is a curve with a horizontal asymptote at y=0 and is symmetrical about the y-axis. The value of C determines the exact position of the curve on the y-axis.
  • #1
calculushelp
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anti derive

20/(1+x^(2))
 
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  • #2
Do you know the derivatives of the inverse trigonometric functions? If so, do you realize that this is very similar to one of them?
 
  • #3
i'm sorry.. i dont
 
  • #5
You really need to be familiar with the common derivatives. You should study them.


That said... if you've learned trigonometric substitution, you should have been able to figure this out without recognizing it.
 

1. What is the formula for the anti derivative of 20/(1+x^(2))?

The formula for the anti derivative of 20/(1+x^(2)) is 20 tan^-1(x) + C, where C is the constant of integration.

2. How do you solve for the anti derivative of 20/(1+x^(2))?

To solve for the anti derivative of 20/(1+x^(2)), you can use the formula 20 tan^-1(x) + C, where C is the constant of integration. You can also use integration by substitution or integration by parts to solve for the anti derivative.

3. What is the significance of the constant of integration in the anti derivative of 20/(1+x^(2))?

The constant of integration, represented by the letter C, is used to account for any possible values of the original function that may have been lost during the process of differentiation. It is added to the result of the anti derivative to ensure that all possible solutions are accounted for.

4. Can the anti derivative of 20/(1+x^(2)) be simplified?

Yes, the anti derivative of 20/(1+x^(2)) can be simplified to 20 tan^-1(x) + C, where C is the constant of integration. However, it is important to note that the constant of integration cannot be simplified further and must be included in the final answer.

5. What is the graph of the anti derivative of 20/(1+x^(2))?

The graph of the anti derivative of 20/(1+x^(2)) is a curve with a horizontal asymptote at y=0 and symmetrical about the y-axis. It approaches positive infinity as x approaches positive infinity and approaches negative infinity as x approaches negative infinity. The value of the constant of integration determines the exact position of the curve on the y-axis.

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