Mastering Integrals: Solving the Anti-Derivative of 7x^-1 with Ease

  • Thread starter Hygelac
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In summary, the anti-derivative of 7x^-1 is 7ln(x) + C, using the fundamental theorem of calculus. However, setting n = -1 will result in dividing by zero, so using the formula \int \frac{1}{u}\,du=\ln|{u}|+C is a better option. This serves as a reminder to always read the whole question before attempting to solve it.
  • #1
Hygelac
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THis one just seems wierd, I know it should be easy but for some reason I am having trouble with it :(

What is the anti-derivative of 7x^-1 ?
 
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  • #2
7ln(x) + C.
 
  • #3
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}+C[/tex]
 
  • #4
Using that won't work in this case.
 
  • #5
i read the q. wrong :P

but sure it works using the fundamental theorem of calculus
 
  • #6
It still doesn't work. If you set n = -1, you'll be dividing by zero...
 
  • #7
[tex]\int \frac{1}{u}\,du=\ln|{u}|+C[/tex]
 
  • #8
Muzza said:
It still doesn't work. If you set n = -1, you'll be dividing by zero...



good point

SEE KIDS what can happen if you don't read the whole question?

*blush* :-p
 

FAQ: Mastering Integrals: Solving the Anti-Derivative of 7x^-1 with Ease

What is an easy integral?

An easy integral is a mathematical concept that involves finding the area under a curve on a graph. It is considered easy when the function being integrated is simple and can be easily solved using basic integration techniques.

How do I solve an easy integral?

To solve an easy integral, you can use basic integration techniques such as the power rule, substitution, or integration by parts. It is also helpful to have a good understanding of basic algebra and trigonometry.

What are some common examples of easy integrals?

Some common examples of easy integrals include integrating polynomials, trigonometric functions, and exponential functions. For example, integrating x^2 or sin(x) would be considered easy integrals.

Why is it important to know how to solve easy integrals?

Knowing how to solve easy integrals is important because it is a fundamental concept in calculus and is used in various fields of science and engineering. It allows us to calculate important quantities such as displacement, velocity, and acceleration.

How can I practice solving easy integrals?

You can practice solving easy integrals by working through different examples and exercises, using online resources and tutorials, and seeking help from a tutor or teacher. It is also helpful to review the basic rules and techniques for integration.

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