What is the integral from 1 to 3 of (e^{3/x})/(x^2) ?

The integral from 1 to 3 of (e^{3/x})/(x^2) is (e^3-e)/3

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integral from 1 to 3 of (e^{3/x})/(x^2)

\int_{1}^{3} \frac{e ^{\frac{3}{x}}}{x ^{2}} d x

\frac{e ^{3} - e}{3}

Decimal

5.78908 \dots

Solution steps

\int_{1}^{3} \frac{e ^{\frac{3}{x}}}{x ^{2}} d x

Apply u-substitution

= \int_{3}^{1} - \frac{e ^{u}}{3} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{3} - \frac{e ^{u}}{3} d u

Take the constant out:

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

= - (- \frac{1}{3} \cdot \int_{1}^{3} e^{u} d u)

Use the common integral:

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

= - (- \frac{1}{3} [e^{u}]_{1}^{3})

Simplify

= \frac{1}{3} [e^{u}]_{1}^{3}

Compute the boundaries:

e^{3} - e

= \frac{1}{3} (e^{3} - e)

Simplify

= \frac{e ^{3} - e}{3}

(3 x + 2 y) d x + (2 x + y) d y = 0

\frac{\partial}{\partial x} (\frac{x + y}{z})

\int cot (x) csc^{2} (x) d x

\frac{1}{x - 1}, x = 20

\frac{d}{d x} (x - \frac{1}{x ^{2}})

What is the integral from 1 to 3 of (e^{3/x})/(x^2) ?
The integral from 1 to 3 of (e^{3/x})/(x^2) is (e^3-e)/3