∫ X²+2/√x³+6x+1 hasil yang kudapat 2/3 (3x²+9x+1) baru coba2 ngga tahu bener apa nggak, sbg perbandingan hasil yg kalian dpt berapa? sertakan cara juga ya!
alvinteguh
U = x³ + 6x + 1 du/dx = 3x² + 6 dx = du / (3x² + 6)
∫ (x² + 2) / √(x³ + 6x + 1) dx = ∫ (x² + 2) / √u . du / (3x² + 6) = ∫ 1/3 . u^-1/2 . du = 1/3 ∫ u^-1/2 . du = 1/3 (1/(1/2) u^1/2 + C) = 1/3 (2 u^1/2) + C = 2/3 u^1/2 + C = 2/3 √(x³ + 6x + 1) + C
du/dx = 3x² + 6
dx = du / (3x² + 6)
∫ (x² + 2) / √(x³ + 6x + 1) dx
= ∫ (x² + 2) / √u . du / (3x² + 6)
= ∫ 1/3 . u^-1/2 . du
= 1/3 ∫ u^-1/2 . du
= 1/3 (1/(1/2) u^1/2 + C)
= 1/3 (2 u^1/2) + C
= 2/3 u^1/2 + C
= 2/3 √(x³ + 6x + 1) + C