Evaluate the integral: integral (x2 dx)/([5]3x3 + 7)

Let $u = 3x^3 + 7$.

Differentiate $u$ with respect to $x$:

So, $du = 9x^2 \, dx$.

From $du = 9x^2 \, dx$, we have $x^2 \, dx = \frac{1}{9} du$.

The original integral is $\int \frac{x^2 \, dx}{\sqrt[5]{3x^3 + 7}}$.
Substitute $u$ and $du$:

Rewrite the term with a negative exponent:

Use the power rule for integration, $\int u^n \, du = \frac{u^{n+1}}{n+1} + C$: