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

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

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

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

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

Solution steps

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

y^{^{'}} + \frac{1}{x} y = x^{2} y^{1}

\int \frac{1}{3 ^{x}} d x

y^{^{'}} = 2 y + 1

cos (t - \frac{2 π}{3})

x \to 0 lim (\frac{7 ^{x} - 4 ^{x}}{x})

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