Question

\[ \int (2x^2 + 3x + 1) \,dx \]

find the antiderivative of the given expression?

Answer 1

∫(2x² + 3x + 1) dx = ∫2x² dx + ∫3x dx + ∫1 dx

Now, apply the power rule for integration:

∫2x² dx = (2/3)x³ ∫3x dx = (3/2)x² ∫1 dx = x

Now, combine these results:

(2/3)x³ + (3/2)x² + x + C

where C is the constant of integration.