solve-x-Inx-dx-

Question Number 185959 by Michaelfaraday last updated on 30/Jan/23

s o l v e :

\int x^{I n x} d x

Answered by Frix last updated on 30/Jan/23

\int x^{\ln x} d x \overset{t = \frac{1}{2} + \ln x}{=} \frac{1}{\sqrt[4]{e}} \int e^{t^{2}} d t = \frac{\sqrt{π}}{2 \sqrt[4]{e}} erfi (t) =

= \frac{\sqrt{π}}{2 \sqrt[4]{e}} erfi (\frac{1}{2} + \ln x) + C

Commented by Michaelfaraday last updated on 30/Jan/23

t h a n k s s i r