What is the integral of (6e^{1/x})/(x^2) ?

The integral of (6e^{1/x})/(x^2) is -6e^{1/x}+C

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integral of (6e^{1/x})/(x^2)

\int \frac{6 e ^{\frac{1}{x}}}{x ^{2}} d x

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

Solution steps

\int \frac{6 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

= 6 \cdot \int \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

Apply u-substitution

: \int - e^{u} d u

= 6 \cdot \int - e^{u} d u

Take the constant out:

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

= 6 (- \int e^{u} d u)

Use the common integral:

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

= 6 (- e^{u})

Substitute back

u = \frac{1}{x}

= 6 (- e^{\frac{1}{x}})

Simplify

= - 6 e^{\frac{1}{x}}

Add a constant to the solution

= - 6 e^{\frac{1}{x}} + C

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What is the integral of (6e^{1/x})/(x^2) ?
The integral of (6e^{1/x})/(x^2) is -6e^{1/x}+C