What is the integral of (5e^{6/(x^4)})/(x^5) ?

The integral of (5e^{6/(x^4)})/(x^5) is -5/24 e^{6/(x^4)}+C

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integral of (5e^{6/(x^4)})/(x^5)

\int \frac{5 e ^{\frac{6}{x ^{4}}}}{x ^{5}} d x

- \frac{5}{24} e^{\frac{6}{x ^{4}}} + C

Solution steps

\int \frac{5 e ^{\frac{6}{x ^{4}}}}{x ^{5}} d x

Take the constant out:

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

= 5 \cdot \int \frac{e ^{\frac{6}{x ^{4}}}}{x ^{5}} d x

Apply u-substitution

: \int \frac{e ^{\frac{6}{u}}}{4 u ^{2}} d u

= 5 \cdot \int \frac{e ^{\frac{6}{u}}}{4 u ^{2}} d u

Take the constant out:

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

= 5 \cdot \frac{1}{4} \cdot \int \frac{e ^{\frac{6}{u}}}{u ^{2}} d u

Apply u-substitution

: \int - \frac{e ^{v}}{6} d v

= 5 \cdot \frac{1}{4} \cdot \int - \frac{e ^{v}}{6} d v

Take the constant out:

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

= 5 \cdot \frac{1}{4} (- \frac{1}{6} \cdot \int e^{v} d v)

Use the common integral:

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

= 5 \cdot \frac{1}{4} (- \frac{1}{6} e^{v})

Substitute back

= 5 \cdot \frac{1}{4} (- \frac{1}{6} e^{\frac{6}{x ^{4}}})

Simplify

5 \cdot \frac{1}{4} (- \frac{1}{6} e^{\frac{6}{x ^{4}}}) : - \frac{5}{24} e^{\frac{6}{x ^{4}}}

= - \frac{5}{24} e^{\frac{6}{x ^{4}}}

Add a constant to the solution

= - \frac{5}{24} e^{\frac{6}{x ^{4}}} + C

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

y = \frac{∣ x ∣}{2 - x ^{2}}, (1, 1)

f (x) = 5 x^{3} sin (x)

\frac{d}{d x} (ln (8 x^{3} - x^{2}))

\frac{d y}{e ^{4 y}} = e^{5 t} d t

What is the integral of (5e^{6/(x^4)})/(x^5) ?
The integral of (5e^{6/(x^4)})/(x^5) is -5/24 e^{6/(x^4)}+C