∫(5x³ - 2x² + 3x)dx = 5x⁴/4 -2x³/3 + 3x²/2 + c
∫(∛x² + √x)dx = ∫(x^⅔)dx + ∫(x^½)dx = (3x^(⁵/₃))/5 + (2x^(³/₂))/3 + c
∫(2x-1)²dx = (1/2)∫u²du = (1/2)*u³/3 = u³/6 = (2x - 1)³/6 + c
u = 2x - 1
du/dx = 2
dx = (1/2)du
∫x³(1+5x)dx = ∫x³dx + 5∫x⁴dx = x⁴/4 + 5x⁵/5 = x⁴/4 + x⁵ + c
∫(3x³-2x² + 6x)dx/2x =∫(1/2)(3x²-2x + 6)dx = (1/2)(x³-x²+x) +c