An indefinite integral

In summary, an indefinite integral is a mathematical concept used to find the original function from its derivative. It is represented by the symbol ∫ and is the reverse operation of differentiation. Unlike a definite integral, it does not have specific limits of integration and results in a general function rather than a numerical value. The process for solving an indefinite integral involves using integration techniques and considering specific rules or formulas. However, not all functions have an indefinite integral due to the lack of an antiderivative or the function being undefined. In science, indefinite integrals are useful for determining the behavior and properties of systems and solving differential equations that model real-world phenomena.
  • #1
mrdoe
36
0
Find
[tex]\displaystyle\int\dfrac{\sec ^2\sqrt{x}}{\sqrt{x}} dx[/tex]
We're supposed to use u du substitution but I can't seem to get this one.

EDIT: Sorry I didn't read rules.

I tried [tex]u=\sec^2\sqrt{x}[/tex] and all variants. Usually it was in the form of

[sec or cos][^2 or none][sqrt x]
 
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  • #2
Well a more intuitive substitution would be to take [tex]u=\sqrt{x}[/tex].
 
  • #3
thanks, I can't see why I didn't see that
 

1. What is an indefinite integral?

An indefinite integral is a mathematical concept used to find the original function from its derivative. It is represented by the symbol ∫ and is the reverse operation of differentiation.

2. How is an indefinite integral different from a definite integral?

A definite integral has specific limits of integration, while an indefinite integral does not. This means that the result of an indefinite integral will be a general function, whereas a definite integral will give a specific numerical value.

3. What is the process for solving an indefinite integral?

The process for solving an indefinite integral involves using integration techniques such as substitution, integration by parts, and trigonometric identities. It is important to also consider any specific rules or formulas for the function being integrated.

4. Can all functions be integrated indefinitely?

No, not all functions have an indefinite integral. This is because the function may not have an antiderivative or the integration may result in a function that is not defined for all values.

5. How are indefinite integrals useful in science?

Indefinite integrals are useful in science for finding the original function from its derivative. This is important in determining the behavior and properties of systems, as well as in solving differential equations that model real-world phenomena.

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