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

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

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

\int x^{2} \cdot 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

\int \frac{e ^{x}}{( e ^{x} - 1 ) ( e ^{2 x} + 1 )} d x

\frac{x}{x ^{2} + 64}

x \to 3 lim (\frac{( x ^{2} - 6 )}{( x - 9 )})

\frac{d}{d x} (lo g_{6} (3 x^{3} + 4 x^{2} + 4 x))

\int 64 - 5 x^{2} d x

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