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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{e ^{u}}{2} d u

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

Use the common integral:

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

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

Substitute back

u = \frac{2}{x}

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

Add a constant to the solution

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

y^{^{'}} + 6 y = 4 x^{3} e^{- 6 x}

\frac{d y}{d x} = 5 + e^{y - 5 x + 1}, y (0) = - 1

x \to 2 + lim (- 1)

\frac{d}{d x} (8 x + x^{2} + 7 x + 3)

e^{17 t} t^{7}

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