To solve the integral 

\[
\int \frac{x^2}{\sqrt{x^2 + 5}} \, dx
\]

we can use a substitution method. Here's the step-by-step process:

### Step 1: Substitution
Let’s set:
\[
u = x^2 + 5
\]
Now, differentiate both sides with respect to \(x\):
\[
du = 2x \, dx
\]

Thus:
\[
\frac{du}{2} = x \, dx
\]

Now, rewrite the original integral in terms of \(u\):

\[
\int \frac{x^2}{\sqrt{x^2 + 5}} \, dx = \int \frac{(u - 5)}{\sqrt{u}} \cdot \frac{du}{2x}
\]

This approach isn't simplifying easily. Let's try to apply integration by parts instead or look into trigonometric substitution

Learn how to solve the integral ∫ (x^2)/(sqrt(x^2 + 5)) dx using substitution and integration by parts. This problem covers key calculus concepts like substitution and trigonometric methods. Suitable for undergraduate calculus students.

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