Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 120531 by A8;15: last updated on 01/Nov/20

Commented by Dwaipayan Shikari last updated on 01/Nov/20

$$\int e^{x^x}dx=\int \underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{{\left(x^x\right)}^n}{n!}dx$$$$=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}\int x^{nx}dx$$$$=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}\int {\left(e^{xlogx}\right)}^{n}dx$$$$=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}\int e^{nxlogx}dx$$$$=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}\int \underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{{\left(nxlogx\right)}^n}{n!}dx$$$$=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}\int n^n{x}^n{log}^{n}xdx$$$$$$$${\int }_0^1{x}^{x}dx=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^n}{{(n+1)}^{(n+1)}}$$

Answered by Lordose last updated on 01/Nov/20

$$\mathrm{I}\mathrm{prefer}\mathrm{you}\mathrm{use}\mathrm{series}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com