What is the integral of (e^{1/(x^6)})/(x^7) ?

The integral of (e^{1/(x^6)})/(x^7) is -1/6 e^{1/(x^6)}+C

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integral of (e^{1/(x^6)})/(x^7)

\int \frac{e ^{\frac{1}{x ^{6}}}}{x ^{7}} d x

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

Solution steps

\int \frac{e ^{\frac{1}{x ^{6}}}}{x ^{7}} d x

Apply u-substitution

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

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

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

Simplify

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

Add a constant to the solution

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

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What is the integral of (e^{1/(x^6)})/(x^7) ?
The integral of (e^{1/(x^6)})/(x^7) is -1/6 e^{1/(x^6)}+C