∫x²(1+3x)dx

1. Expand the integrand: ∫(x² + 3x³) dx.

2. Integrate term by term: ∫x² dx + ∫3x³ dx.

3. x³/3 + 3(x⁴/4) + C = x³/3 + (3x⁴/4) + C.