integrate, ∫ X X dx

integrate,  XX dx


1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Hello Student,
Please find answer to your question below

I = \int x^{x}dx
There is not any standard mathematical expression for this integral.
What we can do is expand the integral function around zero & then do step by step integration upto few terms.
x^{x} = x + \frac{x^{2}}{4}.(2logx)+\frac{x^{3}}{54}.(9log^{2}x-6logx+2)+........
I = \int (x + \frac{x^{2}}{4}.(2logx)+\frac{x^{3}}{54}.(9log^{2}x-6logx+2)+........)dx
I = \int xdx + \int \frac{x^{2}}{4}.(2logx)dx+\int \frac{x^{3}}{54}.(9log^{2}x-6logx+2)dx+........I = \frac{x^{2}}{4} + \frac{x^{3}}{12}.(2logx)-\frac{x^{3}}{18}+\frac{x^{4}}{216}.(9log^{2}x-6logx+2)-........You can apply the ILATE rule furthur to get upto which term you want according to the options.

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