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प्रश्न
Integrate the functions:
`xsqrt(x + 2)`
उत्तर
Let `I = int x sqrt(x + 2)` dx
Taking `sqrt(x + 2) = t`
or x + 2 = t2
or dx = 2t dt
Hence, `I = int (t^2 - 2). t. 2t dt`
`= int 2t^4 - 4t^2 dt`
`= 2 int (t^4 - 2t^2)` dt
`= 2 int t^4 dt - 4 int` t2 dt
`= 2/5 t^5 - 4/3 t^3 + C`
`=> 2/5 (x + 2)^(5/2) - 4/3 (x + 2)^(3/2) + C`
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