Evaluate : ∫4x-6(x2-3x+5)32 dx - Mathematics and Statistics

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Sum

Evaluate :

`int(4x - 6)/(x^2 - 3x + 5)^(3/2)  dx`

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Solution

Let I =`int(2(2x - 3))/(x^2 - 3x + 5)^(3/2)  dx`    ...(Taking 2 common in Numerator)

Put (x2 - 3x + 5) = t

(2x - 3) dx = dt

Let I =`(3dt)/t^(3/2)`

`=2intt^((-3/2)).dt`

`=2[t^((-1/2))/((-1/2))]`

`-4/sqrt(t)+ c`

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