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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int e^{u} d u

= 2 \cdot \int e^{u} d u

Use the common integral:

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

= 2 e^{u}

Substitute back

u = - \frac{1}{x}

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

Add a constant to the solution

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

x \to \infty lim (2 + 3 - 2)

x \to 0 lim (\frac{cos ( x ) - cos ( x )}{x ^{2}})

y^{^{''}} - y^{^{'}} = - 3

\int_{- π}^{π} sin (3 x) sin (3 x) d x

x y^{^{'}} + 2 y = - 1 e^{x}

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