What is the integral of x^4e^{-x^5} ?

The integral of x^4e^{-x^5} is -1/5 e^{-x^5}+C

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integral of x^4e^{-x^5}

\int x^{4} e^{- x^{5}} d x

- \frac{1}{5} e^{- x^{5}} + C

Solution steps

\int x^{4} e^{- x^{5}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{5} d u

= \int - \frac{e ^{u}}{5} d u

Take the constant out:

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

= - \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{5} e^{u}

Substitute back

u = - x^{5}

= - \frac{1}{5} e^{- x^{5}}

Add a constant to the solution

= - \frac{1}{5} e^{- x^{5}} + C

\int \frac{3 x}{2 x ^{2} + 5} d x

\frac{\partial}{\partial x} (cos (- t + y + e^{x}))

\int x^{5} e^{x^{2}} d x

\frac{d}{d x} (ln (cos (ln (x))))

\frac{d y}{d t} = 3 t e^{- y}

What is the integral of x^4e^{-x^5} ?
The integral of x^4e^{-x^5} is -1/5 e^{-x^5}+C