Finding $\int x^xdx$ Ask Question Asked 12 years, 10 months ago. Modified 1 year, 1 month ago. Viewed 155k ...

2023年12月7日 · How would you calculate the following integral? $$\\int_0^1 x^xdx$$ I write my answer below. Don't be shy to speak out if you find the mistakes (if there are any) or have a better solution.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2023年5月8日 · So I was browsing the homepage of Youtube to see if there were any math equations that I thought that I might be able to solve when I came across this video by Dr. Trevor Bazett saying that the Bernoulli integral (this dude $\longrightarrow$ $\int_0^1 x^xdx$) is ridiculous, which I thought that I might be able to do. Here are my attempts at ...

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2021年4月11日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2017年11月16日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

So I asked Mathematica about $\int x^xdx$ and it just has no answer. I looked here :Finding $\int x^xdx$ but my question is a bit different. Hence, if it is possible to solve $\int x^xdx$ explicitly, how can this be done, or does $\int x^x dx$ even exist and if it does not, why is that so?

2017年8月9日 · How does one integrate: $$ I= \int e^x sin^{-1}xdx $$ I've tried doing this by parts but in the end, I just get I=I. Does this mean the function is "unintegratable"(if something as such exists)? PS: I'm very new to calculus so this question might just be stupid. Thanks.

It's because an integral means you are summing over a lot of very thin rectangles under a curve. The height of the rectangle is f(x) and the width is called $\delta x$ (These two symbols should be read as a single symbol, it doesn't mean $\delta \times x$).