What is the integral of (e^{1/(x^8)})/(x^9) ?

The integral of (e^{1/(x^8)})/(x^9) is -1/8 e^{1/(x^8)}+C

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integral of (e^{1/(x^8)})/(x^9)

\int \frac{e ^{\frac{1}{x ^{8}}}}{x ^{9}} d x

- \frac{1}{8} e^{\frac{1}{x ^{8}}} + C

Solution steps

\int \frac{e ^{\frac{1}{x ^{8}}}}{x ^{9}} d x

Apply u-substitution

: \int \frac{e ^{\frac{1}{u}}}{8 u ^{2}} d u

= \int \frac{e ^{\frac{1}{u}}}{8 u ^{2}} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int \frac{e ^{\frac{1}{u}}}{u ^{2}} d u

Apply u-substitution

: \int - e^{v} d v

= \frac{1}{8} \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}{8} (- \int e^{v} d v)

Use the common integral:

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

= \frac{1}{8} (- e^{v})

Substitute back

= \frac{1}{8} (- e^{\frac{1}{x ^{8}}})

Simplify

= - \frac{1}{8} e^{\frac{1}{x ^{8}}}

Add a constant to the solution

= - \frac{1}{8} e^{\frac{1}{x ^{8}}} + C

x \to - 3 lim (\frac{x - 3}{9 x})

\frac{\partial}{\partial x} (x^{2} + 5 x z + 3 y z^{2})

f (x) = 8 ln (t^{8})

y = \frac{cos ( x )}{x ^{5}}

1 + e^{2 x}

What is the integral of (e^{1/(x^8)})/(x^9) ?
The integral of (e^{1/(x^8)})/(x^9) is -1/8 e^{1/(x^8)}+C