`int(dx)/(sqrt(x+1)+sqrt(x+2))`

1.	`int(dx)/(sqrt(x+1)+sqrt(x+2))`
Answer» Correct Answer - `2/3 (x+2)^(3//2) - 2/3(x+1)^(3//2) + C`. `I = int(1)/((sqrt(x+2)+ sqrt(x+1))) xx ((sqrt(x+2) - sqrt(x+1)))/((sqrt(x+2) - sqrt(x+1))) dx` `= intsqrt(x+2) dx - intsqrt(x+1) dx =2/3 (x+2)^(3//2) - 2/3 (x+1)^(3//2) +C`.

Discussion

(i) `int(6x^(5) - 2/(x^(4)) - 7x + 3/x - 5 + 4e^(x) + 7^(x))dx` (ii) `int (8-x+2x^(3) -6/(x^(3)) +2x^(-5) + 5x^(-1)) dx` , (iii) `int (x/a+a/x+x^(a) +a^(x) + ax) dx`
Evaluate `int(secx)/((secx+tanx)) dx`.
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