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

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

Text Solution

Verified by Experts

I=`int(x+2)/(sqrt(x^2+2x+3))dx`
I=1/2`int(2x+2)/(sqrt(x^2+2x+3))dx`+`int(1)/(sqrt(x^2+2x+3))dx`
`I=I_1+I_2`
`I_1=``int(2x+2)/(sqrt(x^2+2x+3))dx`
let `x^2+2x+3=t`
`2x+2dx=dt`
`I_1=int(dt)/sqrt(t)`
`I_1=2sqrt(t)+c`
...
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