Question

Integral parsial ∫ (5ⅹ+2)³ dx = ...

Answer 1

Verified answer

∫ (5ⅹ + 2)³ dx =

Misal :
u = 5x + 2
du/dx = 5 ==> dx = du/5

∫ (5ⅹ + 2)³ dx
= ∫ u³ du/5
= (1/5) ∫ u³ du
= (1/5) . (1/4) u⁴ + C
= (1/20) (5x + 2)⁴ + C


Atau

∫ (ax + b)^n dx
= [(ax + b)^(n + 1)] / [(n + 1) . a] + C

Jadi :

∫ (5ⅹ + 2)³ dx
= (5ⅹ + 2)⁴ / (4.5) + C
= (1/20) (5x + 2)⁴ + C