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

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

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

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

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

Solution steps

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