What is the integral of-6x^2e^{x^3} ?

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

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integral of-6x^2e^{x^3}

\int - 6 x^{2} e^{x^{3}} d x

- 2 e^{x^{3}} + C

Solution steps

\int - 6 x^{2} e^{x^{3}} d x

Take the constant out:

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

= - 6 \cdot \int x^{2} e^{x^{3}} d x

Apply u-substitution

: \int \frac{e ^{u^{\frac{3}{2}}} u}{2 x} d u

= - 6 \cdot \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

= - 6 \cdot \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= - 6 \cdot \frac{1}{3} e^{u}

Substitute back

u = x^{3}

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

Simplify

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

= - 2 e^{x^{3}}

Add a constant to the solution

= - 2 e^{x^{3}} + C

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