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

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

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

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

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

Solution steps

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

Apply u-substitution

= \int \frac{e ^{3 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^{3 u} d u

Apply u-substitution

= \frac{1}{3} \cdot \int e^{v} \frac{1}{3} d v

Take the constant out:

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

= \frac{1}{3} \cdot \frac{1}{3} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{3} \cdot \frac{1}{3} e^{v}

Substitute back

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

Simplify

\frac{1}{3} \cdot \frac{1}{3} e^{3 x^{3}} : \frac{1}{9} e^{3 x^{3}}

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

Add a constant to the solution

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

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