Tolong di jawab soal ulangan

Jawaban:

bab : Integral Tak Tentu dan Turunan

int xⁿ dx → int xⁿ+¹/(n + 1) + C

f(x) = axⁿ → f′(x) = anxⁿ-¹

maka,

a). hasil dari :

int x⁴ dx

int x⁵/5 + C

= ⅕x⁵ + C

b). f(x) = x² – 3x + 7/ 2x – 3

misal :

u = x² – 3x + 7 → u′ = 2x – 3

v = 2x – 3 → v′ = 2

maka,

f′(x) = u′v – uv′ / v²

f′(x) = (2x – 3)(2x – 3) – 2(x² – 3x + 7) / (2x – 3)²

f′(x) = (4x² – 12x + 9) – 2x² + 6x – 14) / (2x – 3)²

f′(x) = 2x² – 6x -5 / (2x – 3)²