What is the integral of (e 1/(x^2))/(x^3) ?

The integral of (e 1/(x^2))/(x^3) is -e/(4x^4)+C

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integral of (e 1/(x^2))/(x^3)

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

- \frac{e}{4 x ^{4}} + C

Solution steps

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

Simplify

\frac{\frac{1}{x ^{2}}}{x ^{3}} : \frac{1}{x ^{5}}

= e \cdot \int \frac{1}{x ^{5}} d x

Apply the Power Rule

= e (- \frac{1}{4 x ^{4}})

Simplify

e (- \frac{1}{4 x ^{4}}) : - \frac{e}{4 x ^{4}}

= - \frac{e}{4 x ^{4}}

Add a constant to the solution

= - \frac{e}{4 x ^{4}} + C

What is the integral of (e 1/(x^2))/(x^3) ?
The integral of (e 1/(x^2))/(x^3) is -e/(4x^4)+C