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Question
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
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Solution
Let I = `int sqrt("x"^2 + 2"x" + 5)` dx
`= int sqrt("x"^2 + 2"x" + 1 + 4)` dx
`= int sqrt(("x + 1")^2 + (2)^2)` dx
`= ("x" + 1)/2 sqrt(("x" + 1)^2 + (2)^2) + (2)^2/2 log |("x + 1") + sqrt(("x + 1")^2 + (2)^2)|` + c
∴ I = `("x" + 1)/2 sqrt("x"^2 + 2"x" + 5) + 2 log |("x + 1") + sqrt("x"^2 + 2"x" + 5)|` + c
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