Find the indefinite integral.
\[
\int \frac{1}{5+3 x^{2}}(6 x) d x
\]
\[
\int \frac{1}{5+3 x^{2}}(6 x) d x=\square
\]

Step 1 ：Given the integral \(\int \frac{1}{5+3 x^{2}}(6 x) d x\).

Step 2 ：This is a standard form of the integral of a function divided by a quadratic function.

Step 3 ：We can solve this by using the formula for the integral of a function divided by a quadratic function. The formula is \(\int \frac{u'(x)}{a+bu^2(x)} dx = \frac{1}{\sqrt{b}} \arctan\left(\frac{u(x)}{\sqrt{b}}\right) + C\) where u(x) is a function, u'(x) is its derivative, and a and b are constants.

Step 4 ：In this case, u(x) = x, u'(x) = 6, a = 5, and b = 3. So we can substitute these values into the formula and calculate the integral.

Step 5 ：The indefinite integral of the function is \(\boxed{\ln(3x^2 + 5) + C}\) where C is the constant of integration.