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

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

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

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

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

Solution steps

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

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 x^{3}

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

Add a constant to the solution

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

\frac{d}{d x} (e^{x} tan (x))

x \to 0 + lim (x^{s i n (3 x)})

\int (1 - cos (\frac{t}{2}))^{2} sin (\frac{t}{2}) d t

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

\frac{d y}{d x} = y - x^{2}

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