What is the integral of x^2e^{-4x^3} ?

The integral of x^2e^{-4x^3} is -1/12 e^{-4x^3}+C

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integral of x^2e^{-4x^3}

\int x^{2} e^{- 4 x^{3}} d x

- \frac{1}{12} e^{- 4 x^{3}} + C

Solution steps

\int x^{2} e^{- 4 x^{3}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{12} d u

= \int - \frac{e ^{u}}{12} d u

Take the constant out:

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

= - \frac{1}{12} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{12} e^{u}

Substitute back

u = - 4 x^{3}

= - \frac{1}{12} e^{- 4 x^{3}}

Add a constant to the solution

= - \frac{1}{12} e^{- 4 x^{3}} + C

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What is the integral of x^2e^{-4x^3} ?
The integral of x^2e^{-4x^3} is -1/12 e^{-4x^3}+C