Minta bantuannya ya :)
Matematika
vickiazwarahmad
Pertanyaan
Minta bantuannya ya :)
1 Jawaban
-
1. Jawaban arsetpopeye
Int (x^5 (2 - x^3)^1/2) dx
= Int x^2 . x^3 (2 - x^3)^1/2 dx
Misal
u = 2 - x^3 => x^3 = 2 - u
du = -3x^2 dx => dx = du/(-3x^2)
= Int x^2 . x^3 . (2 - x^3)^1/2 dx
= Int x^2 . (2 - u) . u^1/2 . du/(-3x^2)
= Int -1/3 u^1/2 (2 - u) du
= Int -2/3 u^1/2 + 1/3 u^3/2 du
= (-2/3)/(3/2) u^(3/2) + (1/3)/(5/2) u^(5/2) + C
= -4/9 u^(3/2) + 2/15 u^(5/2) + C
= -2/3 u^3/2 (2/3 - 1/5 u) + C
= -2/3 u^3/2 (10 - 3u)/15 + C
= -2/45 (2 - x^3)^3/2 (10 - 3(2 - x^3)) + C
= -2/45 (2 - x^3)^3/2 (10 - 6 + 3x^3) + C
= -2/45 (3x^3 + 4) (2 - x^3)^3/2 + C