tentukan hasil integral a.(x+5)² dx b.(x+3) (x-4)² dx c. x^3 (x²-2)^3 d. (x²-3x)²/2x² dx e.x^3 (x^3-x) (2x²-1)² dx

integral
A. ∫(x+5)² dx =
= ∫ x² +10x + 25 dx = 1/3 x³ + 5x² + 25x + c

B. ∫(x+3)(x-4)² dx = ∫ (x+3)(x² -8x + 16) dx = ∫ x³ - 5x² -8x + 48 dx
= 1/4x⁴ - 5/3 x³ - 4x² + 48x + c

C. ∫ x³ (x² - 2)³ dx = ∫x³ (x⁶ -6x⁴ +12x² -8)dx =  ∫ x⁹ - 6x⁷+12x⁵ -8x³ dx
= 1/10 x¹⁰ - 3/4 x⁸ + 2x⁶ - 2x⁴ + c

D. ∫(x²-3x)² /2x² dx = 1/2  ∫ (x⁴ - 6x⁶ -9x²)x⁻² dx = 1/2 ∫ x² -6x⁴ - 9 dx
= 1/2 (1/3 x³ - 6/5 x⁵ -9x) +c
= 1/6 x³ - 3/5 x⁵ - 9/2 x + c

E.∫ x³ (x³ -x) (2x²-1)² dx = ∫ (x⁶ - x⁴)(4x⁴ - 4x² +1) dx
= ∫ 4x¹⁰ + 5x⁶ - x⁴ dx = 4/11 x¹¹ + 5/7 x⁷ - 1/5 x⁵ + c