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

The integral of x^2e^{2x^3+4} is 1/6 e^{2x^3+4}+C

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

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

\frac{1}{6} e^{2 x^{3} + 4} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{6} d u

= \int \frac{1}{6} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{6} u

Substitute back

u = e^{2 x^{3} + 4}

= \frac{1}{6} e^{2 x^{3} + 4}

Add a constant to the solution

= \frac{1}{6} e^{2 x^{3} + 4} + C

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What is the integral of x^2e^{2x^3+4} ?
The integral of x^2e^{2x^3+4} is 1/6 e^{2x^3+4}+C