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

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

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

\int \frac{1}{x ^{2} e ^{\frac{2}{x}}} d x

\frac{1}{2 e ^{\frac{2}{x}}} + C

Solution steps

\int \frac{1}{x ^{2} e ^{\frac{2}{x}}} d x

Apply u-substitution

= \int - \frac{1}{2 e ^{u}} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int \frac{1}{e ^{u}} d u

Apply u-substitution

= - \frac{1}{2} \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

= - \frac{1}{2} (- \frac{1}{v})

Substitute back

= - \frac{1}{2} (- \frac{1}{e ^{\frac{2}{x}}})

Simplify

- \frac{1}{2} (- \frac{1}{e ^{\frac{2}{x}}}) : \frac{1}{2 e ^{\frac{2}{x}}}

= \frac{1}{2 e ^{\frac{2}{x}}}

Add a constant to the solution

= \frac{1}{2 e ^{\frac{2}{x}}} + C

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