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

Question

john_es · Answer

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?

psymon · Answer

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

$$-e^{1/x} + C$$