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Evaluate: int(3x+1)/(sqrt(5-2x-x^2))dx...

Evaluate: `int(3x+1)/(sqrt(5-2x-x^2))dx`

Text Solution

Verified by Experts

I=`int(3x+1)/(sqrt(5-2x-x^2))dx`
I=`int(-3/2(-2x-2-4/3))/(sqrt(5-2x-x^2))dx`
Let `5-2x-x^2=t`
so `(-2-2x)dx=dt`
now,
`I=-3/2int (dt)/(sqrt(t)-2int(dx)/(sqrt(6-(x+1)^2))`
`I=-3/2**2sqrt(t)-2sin^(-1)(x+1)/6 +c`
...
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