What is the integral from-1 to 1 of 1/(x^2)e^{2/x} ?

The integral from-1 to 1 of 1/(x^2)e^{2/x} is diverges

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integral from-1 to 1 of 1/(x^2)e^{2/x}

\int_{- 1}^{1} \frac{1}{x ^{2}} e^{\frac{2}{x}} d x

diverges

Solution steps

\int_{- 1}^{1} \frac{1}{x ^{2}} e^{\frac{2}{x}} d x

Adjust integral based on undefined pointsThere is an undefined point within the boundaries at

: 0

= \int_{- 1}^{0} \frac{1}{x ^{2}} e^{\frac{2}{x}} d x + \int_{0}^{1} \frac{1}{x ^{2}} e^{\frac{2}{x}} d x

\int_{- 1}^{0} \frac{1}{x ^{2}} e^{\frac{2}{x}} d x = \frac{1}{2 e ^{2}}

= \frac{1}{2 e ^{2}} + \int_{0}^{1} \frac{1}{x ^{2}} e^{\frac{2}{x}} d x

\int_{0}^{1} \frac{1}{x ^{2}} e^{\frac{2}{x}} d x =

diverges

= diverges

What is the integral from-1 to 1 of 1/(x^2)e^{2/x} ?
The integral from-1 to 1 of 1/(x^2)e^{2/x} is diverges