Matematika

Pertanyaan

hasil dari integral 2x akar x^2+4 adalah

2 Jawaban

  • ∫2x√(x^2 + 4) dx = ∫2x√(x^2 + 4) d(x^2 + 4)/(2x)
    = ∫√(x^2 + 4) d(x^2 + 4)
    = ∫(x^2 + 4)^(1/2) d(x^2 + 4)
    = 1/(3/2) (x^2 + 4)^(3/2) + c
    = 2/3 (x^2 + 4)^(3/2) + c
    = (2/3)(x^2 + 4)√(x^2 + 4) + c
  • ∫ 2x √(x^2 + 4) dx

    Misal
    u = x^2 + 4
    du = 2x dx => dx = du/(2x)

    ∫ 2x √u du/(2x)
    = ∫ u^1/2 du
    = 1/(3/2) u^(3/2) + C
    = 2/3 u √u + C
    = 2/3 (x^2 + 4) √(x^2 + 4) + C

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