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

The integral of x^2e^{-2x^3} is -1/6 e^{-2x^3}+C

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

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

- \frac{1}{6} e^{- 2 x^{3}} + C

Solution steps

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

Apply u-substitution

: \int - \frac{e ^{u}}{6} d u

= \int - \frac{e ^{u}}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = - 2 x^{3}

= - \frac{1}{6} e^{- 2 x^{3}}

Add a constant to the solution

= - \frac{1}{6} e^{- 2 x^{3}} + C

\int 2 [1 - cos^{2} (2 x)] d x

\int_{- 1}^{1} π (2 - 2 x^{2})^{2} d x

y^{^{''}} + 2 y^{^{'}} - 15 y = 4 e^{- t}

\frac{\partial}{\partial y} (x^{2} - y)

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0

What is the integral of x^2e^{-2x^3} ?
The integral of x^2e^{-2x^3} is -1/6 e^{-2x^3}+C