Evaluate the integral $$ \int (3x^2) \cdot e^{x^3} \, dx $$ using substitution.

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To evaluate the integral $$ \int (3x^2) \cdot e^{x^3} \, dx $$, we can use the substitution method.

Let's choose the substitution:
$$
u = x^3
$$
Then, we need to find $$ du $$:
$$
du = 3x^2 \, dx
$$
This means that:
$$
dx = \frac{du}{3x^2}
$$

Now, we can rewrite the integral in terms of $$ u $$:
$$
\int (3x^2) \cdot e^{x^3} \, dx = \int e^{u} \, du
$$

The integral of $$ e^u $$ is:
$$
\int e^u \, du = e^u + C
$$

Now, we substitute back $$ u = x^3 $$:
$$
e^u + C = e^{x^3} + C
$$

Thus, the final result of the integral is:
$$
\int (3x^2) \cdot e^{x^3} \, dx = e^{x^3} + C
$$
Use substitution with $$ u = x^3 $$ and $$ du = 3x^2 \, dx $$. The integral becomes $$ \int e^u \, du $$, which evaluates to $$ e^u + C $$. Substituting back $$ u = x^3 $$, the result is $$ e^{x^3} + C $$.

Evaluate the integral \( \int (3x^2) \cdot e^{x^3} \, dx \) using substitution.

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