What is the integral of e^{-x^8}x^7 ?

The integral of e^{-x^8}x^7 is -1/8 e^{-x^8}+C

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integral of e^{-x^8}x^7

\int e^{- x^{8}} x^{7} d x

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

Solution steps

\int e^{- x^{8}} x^{7} d x

Apply u-substitution

: \int - \frac{e ^{u}}{8} d u

= \int - \frac{e ^{u}}{8} 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 e^{u} d u

Use the common integral:

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

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

Substitute back

u = - x^{8}

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

Add a constant to the solution

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

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What is the integral of e^{-x^8}x^7 ?
The integral of e^{-x^8}x^7 is -1/8 e^{-x^8}+C