Question

Can anybody help me solve ∫(e^(1/x))(x^-2) Thanks!!!

Answer 1

Rewritting the integral,\[\int e^{x^-1}x^{-2}dx\]You could try a change of variable. For example,\[t=x^{-1}\Rightarrow-dt=x^{-2}dx\]Could you complete it from this point?

Answer 2

Looks like your problem is different than how it was interpretted above.

\[\int\limits_{}^{}e^{1/x}x^{-2}dx= \int\limits_{}^{}\frac{ e^{1/x} }{ x^{2} }dx\]Just let u = 1/x. Then du = -dx/x^2, dx = -x^2du
\[\int\limits_{}^{}\frac{ e^{u} }{ x^{2} }*-x^{2}du = -\int\limits_{}^{}e^{u}du\]

Of course the integral of e^u is just e^u, so no we replace u with what we originally replaced it with an add C

\[-e^{1/x} + C\]