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प्रश्न
Integrate the functions:
`xsqrt(1+ 2x^2)`
उत्तर
Let `I = int x sqrt(1 + 2x^2)` dx
Taking 1 + 2x2 = t
4x dx = dt
or x dx `= 1/4` dt
Hence, `I = int 1/4 t^(1/2) dt = 1/4 int t^(1/2)` dt
`= 1/4 . 2/3 t^(3/2) + C`
`= 1/6 (1 + 2x^2)^(3/2) + C`
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