Solving for the Antiderivative: 2/x - 5e^5x | Math Homework Help

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SUMMARY

The antiderivative of the function 2/x - 5e^5x is correctly calculated as 2ln|x| - e^5x + k, where k represents the constant of integration. The user correctly identifies that the integral of 1/x is ln|x| and applies the integration rules for exponential functions. The solution demonstrates a clear understanding of the integration process, particularly in handling logarithmic and exponential terms.

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Students studying calculus, particularly those focusing on integration techniques, as well as educators seeking to clarify concepts related to antiderivatives and their applications.

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Homework Statement


Sorry I have class at 8 and I am getting myself confused...
What is the anti-derivative of 2/x - 5e^5x


Homework Equations





The Attempt at a Solution


So I did this...
2 * 1/x - 5e^5x
Anti-derivative:
2ln - 5e^5x
 
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Is an Anti-derivative ...another word for Integration?
if 1/x =lnx ...looks like it.
[Int]2/x - [Int]5e^5x
2[int]1/x - 5[int]e^5x
2Lnx - 5[1/5e^5x]
Ans: 2Lnx -e^5x + k

Am I right?
 

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