What is the integral of x^2e^{4x^3} ?

The integral of x^2e^{4x^3} is 1/12 e^{4x^3}+C

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integral of x^2e^{4x^3}

\int x^{2} e^{4 x^{3}} d x

\frac{1}{12} e^{4 x^{3}} + C

Solution steps

\int x^{2} e^{4 x^{3}} d x

Apply u-substitution

: \int \frac{e ^{u}}{12} d u

= \int \frac{e ^{u}}{12} d u

Take the constant out:

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

= \frac{1}{12} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{12} e^{u}

Substitute back

u = 4 x^{3}

= \frac{1}{12} e^{4 x^{3}}

Add a constant to the solution

= \frac{1}{12} e^{4 x^{3}} + C

n = 0 \sum \infty 1^{l n (n)}

y = \frac{1}{2} e^{2 x} + e^{x} + 1

3 sin (4 x)

\frac{d}{d x} (x^{4} + cos (x) + 1)

\int \frac{( 16 - 9 x ^{2} ) ^{\frac{3}{2}}}{x ^{6}} d x

What is the integral of x^2e^{4x^3} ?
The integral of x^2e^{4x^3} is 1/12 e^{4x^3}+C