What is the integral of x^8e^{-x^9} ?

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

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integral of x^8e^{-x^9}

\int x^{8} e^{- x^{9}} d x

- \frac{1}{9} e^{- x^{9}} + C

Solution steps

\int x^{8} e^{- x^{9}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{9} d u

= \int - \frac{e ^{u}}{9} d u

Take the constant out:

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

= - \frac{1}{9} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{9} e^{u}

Substitute back

u = - x^{9}

= - \frac{1}{9} e^{- x^{9}}

Add a constant to the solution

= - \frac{1}{9} e^{- x^{9}} + C

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\frac{d}{d x} ((3 x^{6} + 8 x^{3})^{4})

4 sec^{2} (x) tan^{2} (x) + 2 sec^{4} (x)

\frac{d}{d x} (e^{- \frac{x}{100}})

\int \frac{2 x - 1}{2 x + 3} d x

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