Ghinashoda
Integral (x² + 2x)dx = Integral (x² + 2x)(x^(-1/2)dx x^1/2 = Integral (x^3/2 + 2x^1/2)dx = (2/5)(x^5/2 + 4/3 x^1/2) + C = (2/5)(x²√x + (4/3)√x) + C = 2x²√x + 8√x + C 5 3 atau = (1/15)(6x²√x + 40√x) + C
Integral x(x^1/2 + x^-1/2)dx = Integral (x^3/2 + x^1/2)dx = (2/5)(x^5/2 + (2/3)x^3/2) + C atau = (2/5)(x²√x + (2/3)x√x) + C atau = 2x²√x + 4x√x + C 5 15 atau = (1/15)(6x²√x + 4x√x) + C
kalikan
(x)3/2 + (x)^1/2
tambah 1 jadi
1/5/2 (x)^5/2 + 1/3/2 (x)^3/2
jadi 2/5(x)^5/2 + 2/3(x)^3/2
dicek lagi
x^1/2 = Integral (x^3/2 + 2x^1/2)dx
= (2/5)(x^5/2 + 4/3 x^1/2) + C
= (2/5)(x²√x + (4/3)√x) + C
= 2x²√x + 8√x + C
5 3 atau
= (1/15)(6x²√x + 40√x) + C
Integral x(x^1/2 + x^-1/2)dx = Integral (x^3/2 + x^1/2)dx
= (2/5)(x^5/2 + (2/3)x^3/2) + C atau
= (2/5)(x²√x + (2/3)x√x) + C atau
= 2x²√x + 4x√x + C
5 15 atau
= (1/15)(6x²√x + 4x√x) + C