calculus - Finding $\int x^xdx$ - Mathematics Stack Exchange
Many people have pointed out that the integral you are looking for is equivalent to, $$\sum_{n}^{\infty} \frac{1}{n!} \int_{0}^{x}x^{n}\ln(x)^ndx$$
What is the integral of 1/x? - Mathematics Stack Exchange
Jan 20, 2021 · Answers to the question of the integral of $\frac{1}{x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers. If we …
calculus - Integrating $\int xe^{-x} dx$ without parts
Mar 4, 2016 · Can $\\int xe^{-x} dx$ ever be solved by integration by substitution without using parts. Or does, as I suspect, substitution fail to yield a solution in this case. Seems that we …
calculus - How to calculate the integral of $x^x$ between $0$ and …
How to calculate $\int_0^1 x^x\,dx$ using series? I read from a book that $$\int_0^1 x^x\,dx = 1-\frac{1 ...
calculus - How to integrate $ \int x^n e^x dx$? - Mathematics …
How to integrate $ \int x^n e^x dx$? Ask Question Asked 14 years ago. Modified 3 years, 11 months ago.
calculus - Integrating $e^{f(x)}$ - Mathematics Stack Exchange
So I went down this rabbit hole, and assuming I didn't make a mistake somewhere, figured out a series that theoretically is $\int e^{f(x)}dx$, but it diverges anywhere that $-1 < f'(x) < 1$ and …
calculus - $\int \frac{x^4-1}{x^2\sqrt{x^4+x^2+1}}dx
May 11, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Integral $\\int \\sqrt{1+x^2}dx$ - Mathematics Stack Exchange
Feb 21, 2018 · I was trying to do this integral $$\\int \\sqrt{1+x^2}dx$$ I saw this question and its' use of hyperbolic functions. I did it with binomial differential method since the given integral is …
calculus - How to integrate $\int \sqrt {x^2+a^2}dx
How to integrate $\int \sqrt{x^2+a^2}dx$ Ask Question Asked 12 years, 1 month ago. Modified 2 years ago.
Integrals such as x+y wrt x - Mathematics Stack Exchange
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 …