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

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

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

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

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

Solution steps

\int \frac{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

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

Simplify

\frac{\frac{1}{x}}{x ^{2}} : \frac{1}{x ^{3}}

= e \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

: - \frac{1}{2 x ^{2}}

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

Simplify

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

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

Add a constant to the solution

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

y^{^{'}} + 2 x y = 0

\int sec^{4} (1) d x

f (x) = \frac{4}{1 + x ^{2}}

x y^{2} \frac{d y}{d x} = y^{3} - x^{3}

cos (- 2 t)

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