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calculushelp
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anti derive
20/(1+x^(2))
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.
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.
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.
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.
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.