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

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

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

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

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

Solution steps

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

\frac{\partial}{\partial y} (x y z^{2} tan (y t))

y = 2 - 6 x, at x = - 1

\frac{s}{s ^{2} - 3}

\int_{0}^{3} \frac{3}{2} x x + 1 d x

\int_{2}^{8} - \frac{x}{2} d x

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