What is the antiderivative of x^2 + (5/x^5) +cos9x - e^-7x?

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Discussion Overview

The discussion revolves around finding the antiderivative of the expression x^2 + (5/x^5) + cos(9x) - e^(-7x) and includes a related expression (2x + 5sqrt(x))/x^2. Participants explore integration techniques and basic rules of integration.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about finding the antiderivative of the given expression.
  • Another participant states that the antiderivative of a sum is the sum of the antiderivatives.
  • A follow-up question asks if the original poster is familiar with basic integration rules for powers, exponential, and trigonometric functions.
  • Further advice is given to approach the problem step by step, suggesting to find the antiderivative of each term individually.
  • Participants discuss rewriting the expression (2x + 5sqrt(x))/x^2 in terms of powers, indicating that it can be simplified before integration.

Areas of Agreement / Disagreement

There is no explicit consensus on the solution to the antiderivative, and participants provide varying levels of guidance and clarification without resolving the original poster's confusion.

Contextual Notes

Participants reference basic integration rules and suggest reviewing foundational formulas, indicating that the discussion may depend on the original poster's understanding of these concepts.

sntawkin
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What is the antiderivative of x^2 + (5/x^5) +cos9x - e^-7x? I'm so lost...

and also (2x + 5sqrtx)/ x^2
 
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An anti-derivative of a sum is a sum of anti-derivatives.
 
sntawkin said:
What is the antiderivative of x^2 + (5/x^5) +cos9x - e^-7x? I'm so lost...

and also (2x + 5sqrtx)/ x^2

Well, do you know basic integration rules for powers, exponential, and trigonometric functions?
 
Do it one step at a time (that's what the others are saying). What is the anti-derivative of x2? What is the anti-derivative of 5x-5? What is the anti-derivative of cos(9x)? What is the anti-derivative of e-7x? If you don't know those, you should go back and review your basic formulas.

As for [tex]\frac{2x+ 5\sqrt{x}}{x^2}[/tex], that's really the same as
[tex]\frac{2x}{x^2}+ \frac{5x^{\frac{1}{2}}}{x^2}= 2x^{-1}+ 5x^{-\frac{3}{2}[/tex].
The anti-derivatives of those should be easy- use the first anti-derivative formula you learned!
 

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