What is the integral of z^2e^{-3z^3} ?

The integral of z^2e^{-3z^3} is -1/9 e^{-3z^3}+C

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integral of z^2e^{-3z^3}

\int z^{2} e^{- 3 z^{3}} d z

- \frac{1}{9} e^{- 3 z^{3}} + C

Solution steps

\int z^{2} e^{- 3 z^{3}} d z

Apply u-substitution

: \int - \frac{e ^{u}}{9} d u

= \int - \frac{e ^{u}}{9} d u

Take the constant out:

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

= - \frac{1}{9} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{9} e^{u}

Substitute back

u = - 3 z^{3}

= - \frac{1}{9} e^{- 3 z^{3}}

Add a constant to the solution

= - \frac{1}{9} e^{- 3 z^{3}} + C

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What is the integral of z^2e^{-3z^3} ?
The integral of z^2e^{-3z^3} is -1/9 e^{-3z^3}+C