Hasil dari integral x (2x+5)^1/2 dx
Matematika
Ansep
Pertanyaan
Hasil dari integral x (2x+5)^1/2 dx
1 Jawaban
-
1. Jawaban whongaliem
∫ x (2x + 5)^1/2 dx =
misal : u = 2x + 5 ⇒ 2x = u - 5
du/dx = 2 x = 1/2 .u - 5/2
dx = 1/2 .du
soal dapat ditulis ....
∫ x (2x + )^1/2 dx = ∫ (1/2 u - 5/2) .u^1/2 . 1/2 du
= ∫1/4 u^3/2 - 5/4 u^1/2 du
= 1/4 ∫ u^3/2 - 5 u^1/2 du
= 1/4 { 2/5 u^5/2 - 10/3 u^3/2 } + c
= 1/4 { 2/15 u^3/2 ( 3 u - 25) + c
= 1/30 (u^3/2) (3 u - 25) + c
= 1/30 . u u^1/2 (3u - 25) + c
= 1/30 (2x + 5) (2x + 5)^1/2 { 3 (2x + 5) - 25 + c
= 1/30 (2x + 5) (2x + 5)^1/2 (6x + 15 - 25) + c
= 1/30 (2x + 5) (2x + 5)^1/2 (6x - 10) + c
= 2/30 (2x + 5) (2x + 5)^1/2 (3x - 5) + c
= 1/15 (3x - 5) (2x + 4) (2x + 5)^1/2 + c ..... atau ...
= 1/15 (3x - 5) (2x + 5)^3/2 + c