12 Days of Christmas Integrals: ∫ 1 ÷ (√(x + a) - √(x)) dx, a is a constant
On the Ninth day of Christmas Integrals, the integral featured today is...
∫ 1 ÷ (√(x + a) - √(x)) dx, a is a constant
Multiply by (√(x+a) + √(x)) ÷ (√(x+a) + √(x)):
= ∫ 1 ÷ (√(x + a) - √(x)) ∙ (√(x+a) + √(x)) ÷ (√(x+a) + √(x)) dx
= ∫ (√(x+a) + √(x)) ÷ (x + a - x) dx
= ∫ (√(x+a) + √(x)) ÷ (a) dx
= ∫ √(x + a) ÷ a + √(x) ÷ a dx
= 2/3 ∙ (x + a)^(3/2) + 2/3 ∙ x^(3/2) ÷ a
= 2 ÷ (3 ∙ a) ∙ ((x + a)^(3/2) + x^(3/2))
Eddie
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