Question:
Integral 1 by square root of X + 2 - square root of X + 1 dx
Answer:
Let I = ∫1/{√(x + 2) - √(x + 1)} dx
=> I = ∫{√(x + 2) + √(x + 1)}/[{√(x + 2) - √(x + 1)}*{√(x + 2) + √(x + 1)}] dx
=> I = ∫{√(x + 2) + √(x + 1)}/{(x + 2) - (x + 1)} dx
=> I = ∫{√(x + 2) + √(x + 1)}/(x + 2 - x - 1) dx
=> I = ∫{√(x + 2) + √(x + 1)} dx
=> I = ∫√(x + 2) dx + ∫√(x + 1) dx
=> I = ∫(x + 2)1/2 dx + ∫(x + 1)1/2 dx
=> I = {(x + 2)3/2 }/(3/2) + {(x + 1)3/2 }/(3/2) + C
=> I = {(x + 2)3/2 + (x + 1)3/2 }/(3/2) + C
=> I = (2/3)*{(x + 2)3/2 + (x + 1)3/2 } + C
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