ʃ ((x²+3x+10)/(x-2))dx

jawab
∑ ? 

ubah soal
∫ (x² + 3x + 10) / (x - 2) dx

u = x- 2 --> du = dx
x= u + 2
x² + 3x + 10 = (u+2)² + 3(u+2) + 10 
= u² + 4u + 4 + 3u + 6 + 10
= u² + 7u + 20
∫(x² + 3x +10) /(x -2)  dx = ∫ (u² +7u +20)/(u) du
= ∫ (u² +7u + 20)(u⁻¹) du
= ∫ u + 7 + 20u⁻¹ du
= 1/2 u² + 7u + 20 ln u+ c
= 1/2 (x- 2)² + 7(x-2) + 20 Ln (x-2) + c
= 1/2 (x² - 4x + 4) + 7x - 14  + 20 ln (x - 2) + c
= 1/2 x² - 2x + 2 + 7x - 14 + 20 ln (x -2) +c
= 1/2 x² + 5x - 12 + 20 ln (x -2) + c