Penjelasan dengan langkah-langkah:

no. 1

∫ (3x² + 2x - 4) dx

= 3/(2 + 1) x^(2 + 1) + 2/(1 + 1) x^(1 + 1) - 4x + c

= 3/3 x³ + 2/2 x² - 4x + c

= x³ + x² - 4x + c

no. 2

₀∫² (3x² - 8x + 5) dx

= (x³ - 4x² + 5x) ]²₀

= (2³ - 4(2)² + 5(2)) - (0³ - 4(0)² + 5(0))

= (8 - 16 + 10) - 0

= 2

no. 3

p > 0 dan

((p)² - 3(p)) - (1² - 3(1)) = 12

p² - 3p - (1 - 3) = 12

p² - 3p + 2 - 12 = 0

p² - 3p - 10 = 0

(p + 2)(p - 5) = 0

p = -2 atau p = 5

Karena p > 0, maka nilai p yang memenuhi adalah 5

no. 4

∫ 12x(x² - 3)⁵

= 12x . 1/2x . 1/6 . (x² - 3)⁶ + c

= (x² - 3)⁶ + c

no. 5

∫ 6x√(4x - 3) dx ➡ ∫ 6x(4x - 3)^½ dx

misal :

u = 6x ➡ du = 6 dx

dv = (4x - 3)^½ ➡ v = 1/6(4x - 3)^3/2

maka :

u.dv = u.v - ∫ v.du

u.dv = 6x(1/6(4x - 3)^3/2) - ∫ 1/6(4x - 3)^3/2 . 6 dx

u.dv = x(4x - 3)^3/2 - ∫ (4x - 3)^3/2 + c

u.dv = x(4x - 3)^3/2 - 1/10(4x - 3)^5/2 + c

Semoga Bermanfaat