Question

Bantu jawab pakai cara dan rumus​ nomor 4 aja​

Answer 1

integral

∫xⁿ dx = 1/(n+1) xⁿ⁺¹ + C

cara 1

u = x + 1 → du = dx

x = u - 1

∫x(x + 1)² dx

= ∫u²(u - 1) du

= ∫(u³ - u²) du

= 1/4 u⁴ - 1/3 u³ + C

= 1/4 (x + 1)⁴ - 1/3 (x + 1)³ + C

= 1/12 (x + 1)³ [3(x + 1) - 4] + C

= 1/12 (x + 1)³(3x - 1) + C

•

cara 2

∫x(x + 1)² dx

= ∫x(x² + 2x + 1) dx

= ∫(x³ + 2x² + x) dx

= 1/4 x⁴ + 2/3 x³ + 1/2 x² + C