What is the integral from 0 to 3 of (e^{3/x})/(x^2) ?

The integral from 0 to 3 of (e^{3/x})/(x^2) is diverges

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integral from 0 to 3 of (e^{3/x})/(x^2)

\int_{0}^{3} \frac{e ^{\frac{3}{x}}}{x ^{2}} d x

diverges

Solution steps

\int_{0}^{3} \frac{e ^{\frac{3}{x}}}{x ^{2}} d x

Compute the indefinite integral:

\int \frac{e ^{\frac{3}{x}}}{x ^{2}} d x = - \frac{1}{3} e^{\frac{3}{x}} + C

Compute the boundaries:

\int_{0}^{3} \frac{e ^{\frac{3}{x}}}{x ^{2}} d x =

diverges

= diverges

\int_{0}^{2} \frac{2}{x ^{2}} d x

\int_{0}^{2} (4 x - x^{2} - x^{2}) d x

\int_{4}^{\infty} \frac{3}{x ^{5}} d x

\int_{1}^{3} 2 x^{2} + 3 d x

\int_{0}^{4} \frac{x - 1}{x ^{2} + x - 2} d x

What is the integral from 0 to 3 of (e^{3/x})/(x^2) ?
The integral from 0 to 3 of (e^{3/x})/(x^2) is diverges