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

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

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

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

\frac{1}{7} e^{7 x^{8}} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{56} d u

= 8 \cdot \int \frac{1}{56} d u

Integral of a constant:

\int a d x = a x

= 8 \cdot \frac{1}{56} u

Substitute back

u = e^{7 x^{8}}

= 8 \cdot \frac{1}{56} e^{7 x^{8}}

Simplify

8 \cdot \frac{1}{56} e^{7 x^{8}} : \frac{1}{7} e^{7 x^{8}}

= \frac{1}{7} e^{7 x^{8}}

Add a constant to the solution

= \frac{1}{7} e^{7 x^{8}} + C

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