What is the integral of x^6e^{-x^7} ?

The integral of x^6e^{-x^7} is -1/7 e^{-x^7}+C

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integral of x^6e^{-x^7}

\int x^{6} e^{- x^{7}} d x

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

Solution steps

\int x^{6} e^{- x^{7}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{7} d u

= \int - \frac{e ^{u}}{7} d u

Take the constant out:

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

= - \frac{1}{7} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{7} e^{u}

Substitute back

u = - x^{7}

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

Add a constant to the solution

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

y = x^{2} - 4 x + 3, (1, 0)

\frac{d}{d x} (\frac{x ( 1 + z ( x ) )}{1 - z ( x )})

\frac{d y}{d x} = 5 x e^{6 y}

3 x + 18, x^{2}

x \to \infty lim (x e^{x})

What is the integral of x^6e^{-x^7} ?
The integral of x^6e^{-x^7} is -1/7 e^{-x^7}+C