Jawaban:

Penjelasan:

a. S = integral (anti turunan)

^ = pangkat

V = akar kuadrat

S (5x³ + 3x - 2) dx = (5/(3+1))x^(3+1) + (3/(1+1))x^(1+1) - 2x + c

= (5/4)x⁴ + (3/2)x² - 2x + c

b. S V(3x + 2) dx = ....?

u = 3x + 2

du/dx = 3

S V(3x + 2) dx = ⅓ S u^½ du

= ⅓ (1/(½ + 1)) u^(½ + 1)

= ⅓ (1/(3/2)) u^(3/2)

= ⅓ . ⅔ . (3x + 2)^(1½)

= (2/9) (3x + 2) V(3x + 2) + c

c. S (x V(x² + 3)) dx = ...

u = x² + 3

du/dx = 2x

S (x V(x² + 3)) dx = S (x . u^½) . (du/2x)

= S ½ . u^½ du

= ½ / (½ + 1) u^(½+1)

= ½ / (3/2) u^(3/2)

= ⅓ u^(3/2)

= ⅓ (x² + 3)^(3/2)

= ⅓ V(x² + 3)³ + c

= ⅓ (x² + 3) V(x² + 3) + c