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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{e ^{u}}{3} d u

= \int - \frac{e ^{u}}{3} d u

Take the constant out:

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

= - \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{3} e^{u}

Substitute back

u = - x^{3}

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

Add a constant to the solution

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

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