Question

Bantu jawab pakai cara dan rumus​

Answer 1

Penjelasan dengan langkah-langkah:

3. ∫ (x + 2)/(x² + 4x + 1)² dx

batas = (1, 0)

u = x² + 4x + 1

du/dx = 2x + 4

dx = 1/(2x + 4) du

∫ (x + 2)/(x² + 4x + 1)² dx

= ∫ (x + 2)/u² . 1/(2x + 4) du

= ∫ (x + 2) . u^-2 . 1/2(x + 2) du

= 1/2 . ∫ u^-2 du

= 1/2 . 1/(-2 + 1) . u^-1 + c

= 1/2 . -1/(x² + 4x + 1) + c

= (1/2 . (-1/(1)² + 4(1) + 1)) - (1/2 . (-1/1(0)² + 4(0) + 1))

= -1/12 - (-1/2)

= -1/12 + 6/12

= 5/12

4. ∫ x(x + 1)² dx

= x(x² + 2x + 1)

= x³ + 2x² + x

= 1/4 . x⁴ + 1/3 . 2x³ + 1/2 x² + c

= 1/4x⁴ + 2/3x³ + 1/2x² + c