[x 2 (2x²+1) dx

The integral of x^2*(2x^2+1) dx can be solved using the power rule for integration, which states that the integral of x^n dx is (1/(n+1))*x^(n+1). Here are the steps:

1. Distribute x^2 into the parentheses: ∫(2x^4 + x^2) dx
2. Separate the terms: ∫2x^4 dx + ∫x^2 dx
3. Apply the power rule to each term: (2/5)x^5 + (1/3)x^3 + C

So, the integral of x^2*(2x^2+1) dx is (2/5)x^5 + (1/3)x^3 + C, where C is the constant of integration.