1) la derivada de la funcion y = √x es2) ∫x ^ 5 dx es3) ∫2xdx es4) ∛x dx es5) ∫(2x² - 5x + 3) dx es?

1) y = √x = x ^ (1 / 2)

dy / dx = 1 / 2[x ^ ( - 1 / 2)] = 1 / 2√x

2)∫x ^ 5 dx = (x ^ 6) / 6 + C

3) ∫2xdx = 2∫xdx = 2x² / 2 + C = x² + C

4)∫∛x dx = ∫ x ^ (1 / 3)dx = x ^ (4 / 3) / (4 / 3) + C = 3 / 4 x ^ (4 / 3) + C

5) ∫(2x² - 5x + 3) dx = ∫2x²dx - ∫5xdx + ∫3dx = 2∫x²dx - 5∫xdx + 3∫dx = 2x³ / 3 - 5x² / 2 + 3x + C.