What is the integral of (e^{5/x})/(x^2) ?

The integral of (e^{5/x})/(x^2) is -1/5 e^{5/x}+C

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integral of (e^{5/x})/(x^2)

\int \frac{e ^{\frac{5}{x}}}{x ^{2}} d x

- \frac{1}{5} e^{\frac{5}{x}} + C

Solution steps

\int \frac{e ^{\frac{5}{x}}}{x ^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{5} d u

= \int - \frac{e ^{u}}{5} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - \frac{1}{5} e^{u}

Substitute back

u = \frac{5}{x}

= - \frac{1}{5} e^{\frac{5}{x}}

Add a constant to the solution

= - \frac{1}{5} e^{\frac{5}{x}} + C

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What is the integral of (e^{5/x})/(x^2) ?
The integral of (e^{5/x})/(x^2) is -1/5 e^{5/x}+C