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

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

Text Solution

Verified by Experts

Let `I=int frac{x+2}{(x^{2}+3 x+3) sqrt{x+1}} d x`
Put `x+1=t^{2}`
`d x =2 t . d t` `implies I =2 int frac{(x+1)+1}{[(x^{2}+2 x+1)+x+2] sqrt{x+1}}`
`=2 int frac{(x+1)+1}{[(x+1)^{2}+x+2] sqrt{x+1}}` ...
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