Learn How to Integrate x^x with Ease | Expert Tips and Tricks

Thread starter Derivative86
Start date Oct 4, 2004
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Integrating

In summary, x^x is a mathematical expression representing a variable raised to its own power. It is difficult to integrate due to its lack of a simple algebraic solution, requiring more advanced techniques. The steps to integrate x^x involve rewriting it as e^ln(x^x), using the rule for integrating e^x, and substituting back in the original expression. There are special cases when integrating x^x, but a calculator cannot be used due to its complex nature. Real-world applications of integrating x^x include calculating area under a curve in fields such as physics, engineering, and economics.

Oct 4, 2004

Derivative86

how do you integrate x^x dx? Thx

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Oct 4, 2004

Hurkyl

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Science Advisor

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Approximately.

Oct 4, 2004

Derivative86

Not an elementry function?

Oct 4, 2004

Gokul43201

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Science Advisor

Gold Member

Ummm...I don't think that can be done, except numerically.

Edit : Too little, too late.

Related to Learn How to Integrate x^x with Ease | Expert Tips and Tricks

What is x^x and why is it difficult to integrate?

x^x is a mathematical expression that represents a variable raised to its own power. It is difficult to integrate because it does not have a simple algebraic solution and requires more advanced techniques such as substitution or integration by parts.

What are the steps to integrate x^x?

The first step is to rewrite x^x as e^ln(x^x) using the properties of logarithms. Then, use the rule for integrating e^x to solve for the integral of e^ln(x^x). Finally, substitute back in the original expression for x^x to get the final answer.

Are there any special cases when integrating x^x?

Yes, when x^x is in the form of a constant raised to the power of a variable, such as 3^x, it can be integrated using the formula for exponential functions. However, when the base of the exponent is a variable, such as x^x, more advanced techniques are needed.

Can x^x be integrated using a calculator?

No, x^x cannot be integrated using a calculator because it requires a more complex approach that cannot be programmed into a calculator. It must be solved using mathematical principles and techniques.

What are some real-world applications of integrating x^x?

Integrating x^x is used in various fields such as physics, engineering, and economics. It can be used to calculate the area under a curve, which has many practical applications, such as determining the total distance traveled by an object with changing velocity or the total revenue from a changing product price.