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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 8 \cdot \int x^{7} e^{8 x^{8}} d x

Apply u-substitution

: \int \frac{e ^{u}}{64} d u

= 8 \cdot \int \frac{e ^{u}}{64} d u

Take the constant out:

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

= 8 \cdot \frac{1}{64} \cdot \int e^{u} d u

Use the common integral:

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

= 8 \cdot \frac{1}{64} e^{u}

Substitute back

u = 8 x^{8}

= 8 \cdot \frac{1}{64} e^{8 x^{8}}

Simplify

8 \cdot \frac{1}{64} e^{8 x^{8}} : \frac{1}{8} e^{8 x^{8}}

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

Add a constant to the solution

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

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