What is the integral of x^{27}e^{-x^{28}} ?

The integral of x^{27}e^{-x^{28}} is -1/28 e^{-x^{28}}+C

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integral of x^{27}e^{-x^{28}}

\int x^{27} e^{- x^{28}} d x

- \frac{1}{28} e^{- x^{28}} + C

Solution steps

\int x^{27} e^{- x^{28}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{28} d u

= \int - \frac{e ^{u}}{28} d u

Take the constant out:

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

= - \frac{1}{28} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{28} e^{u}

Substitute back

u = - x^{28}

= - \frac{1}{28} e^{- x^{28}}

Add a constant to the solution

= - \frac{1}{28} e^{- x^{28}} + C

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What is the integral of x^{27}e^{-x^{28}} ?
The integral of x^{27}e^{-x^{28}} is -1/28 e^{-x^{28}}+C