What is the integral of (e^{1/(x^5)})/(x^6) ?

The integral of (e^{1/(x^5)})/(x^6) is -1/5 e^{1/(x^5)}+C

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integral of (e^{1/(x^5)})/(x^6)

\int \frac{e ^{\frac{1}{x ^{5}}}}{x ^{6}} d x

- \frac{1}{5} e^{\frac{1}{x ^{5}}} + C

Solution steps

\int \frac{e ^{\frac{1}{x ^{5}}}}{x ^{6}} d x

Apply u-substitution

: \int \frac{e ^{\frac{1}{u}}}{5 u ^{2}} d u

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

Take the constant out:

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

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

Apply u-substitution

: \int - e^{v} d v

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

Use the common integral:

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

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

Substitute back

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

Simplify

= - \frac{1}{5} e^{\frac{1}{x ^{5}}}

Add a constant to the solution

= - \frac{1}{5} e^{\frac{1}{x ^{5}}} + C

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\int_{0}^{1} \frac{3}{1 + x ^{2}} d x

\int_{0}^{1} x (x^{2} + 1)^{3} d x

\int ln (e x) d x

x \to 1 lim (x^{2} - x + 1)

What is the integral of (e^{1/(x^5)})/(x^6) ?
The integral of (e^{1/(x^5)})/(x^6) is -1/5 e^{1/(x^5)}+C