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Evaluate: int(2x-5)\ sqrt(x^2-4x+3)\ dx...

Evaluate: `int(2x-5)\ sqrt(x^2-4x+3)\ dx`

Text Solution

Verified by Experts

Let `I=int(2 x-5) sqrt{x^{2}-4 x+3} {dx}`
`=int(2 x-4-1) sqrt{x^{2}-4 x+3} {dx}`
`=int(2 x-4) sqrt{x^{2}-4 x+3} {dx}-int sqrt{x^{2}-4 x+3} {dx}`
`=int(2 x-4) sqrt{x^{2}-4 x+3} {dx}-int sqrt{x^{2}-4 x+4-4+3} {dx}`
`=int(2 x-4) sqrt{x^{2}-4 x+3} {dx}-int sqrt{(x-2)^{2}-1^{2}} d x`
Let `x^{2}-4 x+3=t`
`Rightarrow(2 x-4) d x=d t`
`therefore I=int sqrt{t} {dt}-int sqrt{(x-2)^{2}-1^{2}} d x`
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