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

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

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

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

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

Solution steps

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

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 = - t^{5}

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

Add a constant to the solution

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

\frac{d ^{2}}{d x ^{2}} (- e^{- x^{2}})

\frac{\partial}{\partial x} (A x + B y + C x^{2} y)

5 t^{2}

x \to - 6 - lim (\frac{∣ x + 6 ∣}{x + 6})

\int_{0}^{1} (x^{2} + 1) d x

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