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

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

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

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

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

Solution steps

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

Apply u-substitution

= \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 = - t^{3}

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

Add a constant to the solution

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

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