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What is the definite integral of x^x from 0 to 2?

12.06.2025 00:00

What is the definite integral of x^x from 0 to 2?

I can compute this numerically for you. Let's do that.

The definite integral of xxx^x from 0 to 2 is approximately 2.83392.8339, with a very small error estimate of about 2.66×10−102.66 \times 10^{-10}. ​

I=∫02xx dxI = \int_0^2 x^x \, dx

Why do nearly all of the answers on Quora have “read more” and when I click on it, I get a virus warning every time? Has anyone else had this happen?

The integral of xxx^x from 0 to 2 does not have a simple closed-form solution using elementary functions. However, it can be computed numerically. The definite integral you're asking for is: