How do you integrate $(\frac{e^{\frac{1}{x^{8}}}}{x^{9}}) d x$ $((e^(1/x^8)) / x^9 ) dx$ ?

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Answer 1 · 2018-04-22T17:26:50

$- \frac{1}{8} e^{\frac{1}{x^{8}}} + C$ $-1/8e^(1/x^8)+C$ .

Subst. $\frac{1}{x^{8}} = x^{- 8} = y$ $1/x^8=x^-8=y$

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

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

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

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

$=-1/8e^y$ ,

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

How do you integrate ((e^(1/x^8)) / x^9 ) dx(e1x8x9)dx((e^(1/x^8)) / x^9 ) dx?