Question

How do you integrate `((e^(1/x^8)) / x^9 ) dx`?

Answer 1

`-1/8e^(1/x^8)+C`.

Explanation:

Subst. `1/x^8=x^-8=y`

`:. -8x^(-8-1)dx=-8/x^9dx=dy`.

`:. 1/x^9dx=-1/8dy`.

`:. inte^(1/x^8)/x^9dx`,

`=int-1/8e^y dy`,

`=-1/8e^y`,

`=-1/8e^(1/x^8)+C`.